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\begin{document}

\pagestyle{fancy}
\fancyhead{}
\lhead{Chenyue (22035026)}
\chead{answers one}
\rhead{2020.10.27}


\section*{I.Output six plots for n = 64 }

The six figures are shown below:

\begin{figure}[h]
\begin{minipage}[t]{0.45\linewidth}
\centering
\includegraphics[width=9cm,height=5cm]{NSoDEhwk1_1.eps}
\caption{\qquad The case of$ (v_{1},v_{2})=(0,0)$}
\end{minipage}
\begin{minipage}[t]{0.45\linewidth}        %图片占用一行宽度的45%
\hspace{2mm}
\includegraphics[width=9cm,height=5cm]{NSoDEhwk1_2.eps}
\caption{\qquad The case of$ (v_{1},v_{2})=(0,2)$}
\end{minipage}
\end{figure}

\begin{figure}[h]
\begin{minipage}[t]{0.45\linewidth}
\centering
\includegraphics[width=9cm,height=5cm]{NSoDEhwk1_3.eps}
\caption{\qquad The case of$ (v_{1},v_{2})=(1,1)$}
\end{minipage}
\begin{minipage}[t]{0.45\linewidth}        %图片占用一行宽度的45%
\hspace{2mm}
\includegraphics[width=9cm,height=5cm]{NSoDEhwk1_4.eps}
\caption{\qquad The case of$ (v_{1},v_{2})=(2,0)$}
\end{minipage}
\end{figure}

\begin{figure}[h]
\begin{minipage}[t]{0.45\linewidth}
\centering
\includegraphics[width=9cm,height=5cm]{NSoDEhwk1_5.eps}
\caption{\qquad The case of$ (v_{1},v_{2})=(2,2)$}
\end{minipage}
\begin{minipage}[t]{0.45\linewidth}        %图片占用一行宽度的45%
\hspace{2mm}
\includegraphics[width=9cm,height=5cm]{NSoDEhwk1_6.eps}
\caption{\qquad The case of$ (v_{1},v_{2})=(4,0)$}
\end{minipage}
\end{figure}


\section*{II}

See the C++ code for the specific results.

\section*{III.Report the residual and the reduction rate of the
residuals for each V-cycle. Report the maximum
norm of the error vector and the corresponding con-
vergence rates on the four grids.}

Since the dimension of residual is too large, we only show its maximum norm.The maximum norm of residuals and errors is shown below.

n is the number of intervals plus one! Cycletype 0 means V Cycle, 1 represents FMG Cycle; RO = 0 means full-weight, 1 for injection; IO = 0 for linear, 1 for Quadric.

\subsection*{III-a n=129,RO=0,IO=0,cycletype=0}

The maximum norm of residuals and errors is shown below.

The 1-th V cycle:

The maximum norm of residuals after 1 times V cycle=1198.55

The 1-th residual reduction rate is about 0.984232

The maximum norm of error after 1 times V cycle=2.2798

The 2-th V cycle:

The maximum norm of residuals after 2 times V cycle=20.7267

The 2-th residual reduction rate is about 0.982707

The maximum norm of error after 2 times V cycle=0.127734

The 3-th V cycle:

The maximum norm of residuals after 3 times V cycle=0.446278

The 3-th residual reduction rate is about 0.978468

The maximum norm of error after 3 times V cycle=0.00424629

The 4-th V cycle:

The maximum norm of residuals after 4 times V cycle=0.0122149

The 4-th residual reduction rate is about 0.972629

The maximum norm of error after 4 times V cycle=0.000154757

The 5-th V cycle:

The maximum norm of residuals after 5 times V cycle=0.000410165

The 5-th residual reduction rate is about 0.966421

The maximum norm of error after 5 times V cycle=5.53173e-06

The 6-th V cycle:

The maximum norm of residuals after 6 times V cycle=1.24901e-05

The 6-th residual reduction rate is about 0.969548

The maximum norm of error after 6 times V cycle=1.95072e-07

The 7-th V cycle:

The maximum norm of residuals after 7 times V cycle=4.23146e-07

The 7-th residual reduction rate is about 0.966122

The maximum norm of error after 7 times V cycle=6.73317e-09

Obviously, the maximum norm of error has second-order convergence.

\subsection*{III-b n=129,RO=0,IO=0,cycletype=1}

The maximum norm of residuals and errors is shown below.

The 1-th FMG cycle:

The maximum norm of residuals after 1 times FMG cycle=2122.65

The 1-th residual reduction rate is about 0.972075

The maximum norm of error after 1 times FMG cycle=2.73836

The 2-th FMG cycle:

The maximum norm of residuals after 2 times FMG cycle=318.711

The 2-th residual reduction rate is about 0.849853

The maximum norm of error after 2 times FMG cycle=0.565172

The 3-th FMG cycle:

The maximum norm of residuals after 3 times FMG cycle=74.164

The 3-th residual reduction rate is about 0.7673

The maximum norm of error after 3 times FMG cycle=0.175379

The 4-th FMG cycle:

The maximum norm of residuals after 4 times FMG cycle=22.6228

The 4-th residual reduction rate is about 0.694962

The maximum norm of error after 4 times FMG cycle=0.0631725

The 5-th FMG cycle:

The maximum norm of residuals after 5 times FMG cycle=7.08223

The 5-th residual reduction rate is about 0.686943

The maximum norm of error after 5 times FMG cycle=0.0229192

The 6-th FMG cycle:

The maximum norm of residuals after 6 times FMG cycle=2.2632

The 6-th residual reduction rate is about 0.680439

The maximum norm of error after 6 times FMG cycle=0.00835036

The 7-th FMG cycle:

The maximum norm of residuals after 7 times FMG cycle=0.735114

The 7-th residual reduction rate is about 0.675189

The maximum norm of error after 7 times FMG cycle=0.00304376

The 8-th FMG cycle:

The maximum norm of residuals after 8 times FMG cycle=0.241903

The 8-th residual reduction rate is about 0.670932

The maximum norm of error after 8 times FMG cycle=0.00110927

The 9-th FMG cycle:

The maximum norm of residuals after 9 times FMG cycle=0.0804443

The 9-th residual reduction rate is about 0.667452

The maximum norm of error after 9 times FMG cycle=0.000402984

The 10-th FMG cycle:

The maximum norm of residuals after 10 times FMG cycle=0.0269828

The 10-th residual reduction rate is about 0.664577

The maximum norm of error after 10 times FMG cycle=0.000146071

The 11-th FMG cycle:

The maximum norm of residuals after 11 times FMG cycle=0.00911553

The 11-th residual reduction rate is about 0.662173

The maximum norm of error after 11 times FMG cycle=5.28039e-05

The 12-th FMG cycle:

The maximum norm of residuals after 12 times FMG cycle=0.00309809

The 12-th residual reduction rate is about 0.660131

The maximum norm of error after 12 times FMG cycle=1.90273e-05

The 13-th FMG cycle:

The maximum norm of residuals after 13 times FMG cycle=0.00105842

The 13-th residual reduction rate is about 0.658365

The maximum norm of error after 13 times FMG cycle=6.83556e-06

The 14-th FMG cycle:

The maximum norm of residuals after 14 times FMG cycle=0.000363238

The 14-th residual reduction rate is about 0.65681

The maximum norm of error after 14 times FMG cycle=2.44868e-06

The 15-th FMG cycle:

The maximum norm of residuals after 15 times FMG cycle=0.000125168

The 15-th residual reduction rate is about 0.655412

The maximum norm of error after 15 times FMG cycle=8.74831e-07

The 16-th FMG cycle:

The maximum norm of residuals after 16 times FMG cycle=4.32916e-05

The 16-th residual reduction rate is about 0.654131

The maximum norm of error after 16 times FMG cycle=3.11771e-07

The 17-th FMG cycle:

The maximum norm of residuals after 17 times FMG cycle=1.51565e-05

The 17-th residual reduction rate is about 0.649898

The maximum norm of error after 17 times FMG cycle=1.10858e-07

The 18-th FMG cycle:

The maximum norm of residuals after 18 times FMG cycle=5.33076e-06

The 18-th residual reduction rate is about 0.648285

The maximum norm of error after 18 times FMG cycle=3.93408e-08

The 19-th FMG cycle:

The maximum norm of residuals after 19 times FMG cycle=1.87936e-06

The 19-th residual reduction rate is about 0.647451

The maximum norm of error after 19 times FMG cycle=1.39384e-08

The 20-th FMG cycle:

The maximum norm of residuals after 20 times FMG cycle=6.64108e-07

The 20-th residual reduction rate is about 0.64663

The maximum norm of error after 20 times FMG cycle=4.93234e-09

Obviously, the maximum norm of error has first-order convergence.

\subsection*{III-c n=129,RO=0,IO=1,cycletype=0}

The maximum norm of residuals and errors is shown below.

The 1-th V cycle:

The maximum norm of residuals after 1 times V cycle=712.182

The 1-th residual reduction rate is about 0.990631

The maximum norm of error after 1 times V cycle=2.32715

The 2-th V cycle:

The maximum norm of residuals after 2 times V cycle=16.1559

The 2-th residual reduction rate is about 0.977315

The maximum norm of error after 2 times V cycle=0.0272222

The 3-th V cycle:

The maximum norm of residuals after 3 times V cycle=0.172321

The 3-th residual reduction rate is about 0.989334

The maximum norm of error after 3 times V cycle=0.000979417

The 4-th V cycle:

The maximum norm of residuals after 4 times V cycle=0.00423134

The 4-th residual reduction rate is about 0.975445

The maximum norm of error after 4 times V cycle=1.66835e-05

The 5-th V cycle:

The maximum norm of residuals after 5 times V cycle=8.61233e-05

The 5-th residual reduction rate is about 0.979646

The maximum norm of error after 5 times V cycle=3.97619e-07

The 6-th V cycle:

The maximum norm of residuals after 6 times V cycle=1.815e-06

The 6-th residual reduction rate is about 0.978926

The maximum norm of error after 6 times V cycle=1.13196e-08

The 7-th V cycle:

The maximum norm of residuals after 7 times V cycle=4.28066e-08

The 7-th residual reduction rate is about 0.976415

The maximum norm of error after 7 times V cycle=1.94368e-10

Obviously, the maximum norm of error has second-order convergence.

\subsection*{III-d n=129,RO=0,IO=1,cycletype=1}

The maximum norm of residuals and errors is shown below.

The 1-th FMG cycle:

The maximum norm of residuals after 1 times FMG cycle=3134.55

The 1-th residual reduction rate is about 0.958763

The maximum norm of error after 1 times FMG cycle=3.00464

The 2-th FMG cycle:

The maximum norm of residuals after 2 times FMG cycle=731.753

The 2-th residual reduction rate is about 0.766552

The maximum norm of error after 2 times FMG cycle=0.942051

The 3-th FMG cycle:

The maximum norm of residuals after 3 times FMG cycle=188.899

The 3-th residual reduction rate is about 0.741854

The maximum norm of error after 3 times FMG cycle=0.328689

The 4-th FMG cycle:

The maximum norm of residuals after 4 times FMG cycle=57.6185

The 4-th residual reduction rate is about 0.694978

The maximum norm of error after 4 times FMG cycle=0.128749

The 5-th FMG cycle:

The maximum norm of residuals after 5 times FMG cycle=20.9023

The 5-th residual reduction rate is about 0.637229

The maximum norm of error after 5 times FMG cycle=0.0571434

The 6-th FMG cycle:

The maximum norm of residuals after 6 times FMG cycle=7.90218

The 6-th residual reduction rate is about 0.621947

The maximum norm of error after 6 times FMG cycle=0.025502

The 7-th FMG cycle:

The maximum norm of residuals after 7 times FMG cycle=3.1593

The 7-th residual reduction rate is about 0.600199

The maximum norm of error after 7 times FMG cycle=0.0114152

The 8-th FMG cycle:

The maximum norm of residuals after 8 times FMG cycle=1.28297

The 8-th residual reduction rate is about 0.593908

The maximum norm of error after 8 times FMG cycle=0.00513976

The 9-th FMG cycle:

The maximum norm of residuals after 9 times FMG cycle=0.527591

The 9-th residual reduction rate is about 0.588773

The maximum norm of error after 9 times FMG cycle=0.00232219

The 10-th FMG cycle:

The maximum norm of residuals after 10 times FMG cycle=0.219179

The 10-th residual reduction rate is about 0.584566

The maximum norm of error after 10 times FMG cycle=0.00105412

The 11-th FMG cycle:

The maximum norm of residuals after 11 times FMG cycle=0.0918211

The 11-th residual reduction rate is about 0.581068

The maximum norm of error after 11 times FMG cycle=0.000480364

The 12-th FMG cycle:

The maximum norm of residuals after 12 times FMG cycle=0.0387405

The 12-th residual reduction rate is about 0.578087

The maximum norm of error after 12 times FMG cycle=0.000219523

The 13-th FMG cycle:

The maximum norm of residuals after 13 times FMG cycle=0.0164464

The 13-th residual reduction rate is about 0.575472

The maximum norm of error after 13 times FMG cycle=0.000100455

The 14-th FMG cycle:

The maximum norm of residuals after 14 times FMG cycle=0.00702078

The 14-th residual reduction rate is about 0.573112

The maximum norm of error after 14 times FMG cycle=4.60139e-05

The 15-th FMG cycle:

The maximum norm of residuals after 15 times FMG cycle=0.0030124

The 15-th residual reduction rate is about 0.570931

The maximum norm of error after 15 times FMG cycle=2.10581e-05

The 16-th FMG cycle:

The maximum norm of residuals after 16 times FMG cycle=0.00129869

The 16-th residual reduction rate is about 0.568884

The maximum norm of error after 16 times FMG cycle=9.62496e-06

The 17-th FMG cycle:

The maximum norm of residuals after 17 times FMG cycle=0.000562403

The 17-th residual reduction rate is about 0.566947

The maximum norm of error after 17 times FMG cycle=4.38883e-06

The 18-th FMG cycle:

The maximum norm of residuals after 18 times FMG cycle=0.000244579

The 18-th residual reduction rate is about 0.565118

The maximum norm of error after 18 times FMG cycle=1.99647e-06

The 19-th FMG cycle:

The maximum norm of residuals after 19 times FMG cycle=0.000106782

The 19-th residual reduction rate is about 0.563404

The maximum norm of error after 19 times FMG cycle=9.05348e-07

The 20-th FMG cycle:

The maximum norm of residuals after 20 times FMG cycle=4.67901e-05

The 20-th residual reduction rate is about 0.561817

The maximum norm of error after 20 times FMG cycle=4.09212e-07

The 21-th FMG cycle:

The maximum norm of residuals after 21 times FMG cycle=2.05701e-05

The 21-th residual reduction rate is about 0.560375

The maximum norm of error after 21 times FMG cycle=1.84344e-07

The 22-th FMG cycle:

The maximum norm of residuals after 22 times FMG cycle=9.06954e-06

The 22-th residual reduction rate is about 0.559091

The maximum norm of error after 22 times FMG cycle=8.27645e-08

The 23-th FMG cycle:

The maximum norm of residuals after 23 times FMG cycle=4.00896e-06

The 23-th residual reduction rate is about 0.557976

The maximum norm of error after 23 times FMG cycle=3.70342e-08

The 24-th FMG cycle:

The maximum norm of residuals after 24 times FMG cycle=1.77582e-06

The 24-th residual reduction rate is about 0.557038

The maximum norm of error after 24 times FMG cycle=1.65167e-08

The 25-th FMG cycle:

The maximum norm of residuals after 25 times FMG cycle=7.87977e-07

The 25-th residual reduction rate is about 0.556274

The maximum norm of error after 25 times FMG cycle=7.34225e-09

Obviously, the maximum norm of error has first-order convergence.

\subsection*{III-e n=129,RO=1,IO=0,cycletype=0}

The maximum norm of residuals and errors is shown below.

The 1-th V cycle:

The maximum norm of residuals after 1 times V cycle=2438.32

The 1-th residual reduction rate is about 0.967922

The maximum norm of error after 1 times V cycle=1.96618

The 2-th V cycle:

The maximum norm of residuals after 2 times V cycle=167.344

The 2-th residual reduction rate is about 0.931369

The maximum norm of error after 2 times V cycle=1.72869

The 3-th V cycle:

The maximum norm of residuals after 3 times V cycle=13.0748

The 3-th residual reduction rate is about 0.921869

The maximum norm of error after 3 times V cycle=0.0486256

The 4-th V cycle:

The maximum norm of residuals after 4 times V cycle=1.32049

The 4-th residual reduction rate is about 0.899005

The maximum norm of error after 4 times V cycle=0.0408312

The 5-th V cycle:

The maximum norm of residuals after 5 times V cycle=0.112277

The 5-th residual reduction rate is about 0.914973

The maximum norm of error after 5 times V cycle=0.000801272

The 6-th V cycle:

The maximum norm of residuals after 6 times V cycle=0.0117891

The 6-th residual reduction rate is about 0.895

The maximum norm of error after 6 times V cycle=0.000691272

The 7-th V cycle:

The maximum norm of residuals after 7 times V cycle=0.00119609

The 7-th residual reduction rate is about 0.898543

The maximum norm of error after 7 times V cycle=8.11482e-06

The 8-th V cycle:

The maximum norm of residuals after 8 times V cycle=0.000129773

The 8-th residual reduction rate is about 0.891502

The maximum norm of error after 8 times V cycle=1.03922e-05

The 9-th V cycle:

The maximum norm of residuals after 9 times V cycle=1.14379e-05

The 9-th residual reduction rate is about 0.911862

The maximum norm of error after 9 times V cycle=1.29204e-07

The 10-th V cycle:

The maximum norm of residuals after 10 times V cycle=1.41649e-06

The 10-th residual reduction rate is about 0.876159

The maximum norm of error after 10 times V cycle=1.47353e-07

The 11-th V cycle:

The maximum norm of residuals after 11 times V cycle=1.33744e-07

The 11-th residual reduction rate is about 0.905581

The maximum norm of error after 11 times V cycle=1.52836e-09

Obviously, the maximum norm of error has second-order convergence.

\subsection*{III-f n=129,RO=1,IO=0,cycletype=1}

The maximum norm of residuals and errors is shown below.

The 1-th FMG cycle:

The maximum norm of residuals after 1 times FMG cycle=3562.72

The 1-th residual reduction rate is about 0.95313

The maximum norm of error after 1 times FMG cycle=1.68591

The 2-th FMG cycle:

The maximum norm of residuals after 2 times FMG cycle=1251.58

The 2-th residual reduction rate is about 0.648701

The maximum norm of error after 2 times FMG cycle=2.41562

The 3-th FMG cycle:

The maximum norm of residuals after 3 times FMG cycle=684.106

The 3-th residual reduction rate is about 0.453406

The maximum norm of error after 3 times FMG cycle=3.16614

The 4-th FMG cycle:

The maximum norm of residuals after 4 times FMG cycle=460.737

The 4-th residual reduction rate is about 0.326513

The maximum norm of error after 4 times FMG cycle=2.18602

The 5-th FMG cycle:

The maximum norm of residuals after 5 times FMG cycle=281.784

The 5-th residual reduction rate is about 0.388407

The maximum norm of error after 5 times FMG cycle=2.51409

The 6-th FMG cycle:

The maximum norm of residuals after 6 times FMG cycle=245.526

The 6-th residual reduction rate is about 0.128671

The maximum norm of error after 6 times FMG cycle=2.64986

The 7-th FMG cycle:

The maximum norm of residuals after 7 times FMG cycle=188.585

The 7-th residual reduction rate is about 0.231916

The maximum norm of error after 7 times FMG cycle=2.2118

The 8-th FMG cycle:

The maximum norm of residuals after 8 times FMG cycle=132.732

The 8-th residual reduction rate is about 0.296167

The maximum norm of error after 8 times FMG cycle=1.83224

The 9-th FMG cycle:

The maximum norm of residuals after 9 times FMG cycle=87.8016

The 9-th residual reduction rate is about 0.338506

The maximum norm of error after 9 times FMG cycle=1.66355

The 10-th FMG cycle:

The maximum norm of residuals after 10 times FMG cycle=57.0472

The 10-th residual reduction rate is about 0.350272

The maximum norm of error after 10 times FMG cycle=1.70717

The 11-th FMG cycle:

The maximum norm of residuals after 11 times FMG cycle=42.1427

The 11-th residual reduction rate is about 0.261266

The maximum norm of error after 11 times FMG cycle=1.99044

The 12-th FMG cycle:

The maximum norm of residuals after 12 times FMG cycle=34.5243

The 12-th residual reduction rate is about 0.180776

The maximum norm of error after 12 times FMG cycle=2.04388

The 13-th FMG cycle:

The maximum norm of residuals after 13 times FMG cycle=32.3478

The 13-th residual reduction rate is about 0.0630425

The maximum norm of error after 13 times FMG cycle=1.89977

The 14-th FMG cycle:

The maximum norm of residuals after 14 times FMG cycle=27.5499

The 14-th residual reduction rate is about 0.148324

The maximum norm of error after 14 times FMG cycle=1.63536

The 15-th FMG cycle:

The maximum norm of residuals after 15 times FMG cycle=21.8067

The 15-th residual reduction rate is about 0.208465

The maximum norm of error after 15 times FMG cycle=1.31996

The 16-th FMG cycle:

The maximum norm of residuals after 16 times FMG cycle=16.2649

The 16-th residual reduction rate is about 0.254131

The maximum norm of error after 16 times FMG cycle=1.0093

The 17-th FMG cycle:

The maximum norm of residuals after 17 times FMG cycle=12.5072

The 17-th residual reduction rate is about 0.23103

The maximum norm of error after 17 times FMG cycle=0.737539

The 18-th FMG cycle:

The maximum norm of residuals after 18 times FMG cycle=9.61723

The 18-th residual reduction rate is about 0.231067

The maximum norm of error after 18 times FMG cycle=0.52044

The 19-th FMG cycle:

The maximum norm of residuals after 19 times FMG cycle=7.02787

The 19-th residual reduction rate is about 0.269242

The maximum norm of error after 19 times FMG cycle=0.358215

The 20-th FMG cycle:

The maximum norm of residuals after 20 times FMG cycle=4.88973

The 20-th residual reduction rate is about 0.304237

The maximum norm of error after 20 times FMG cycle=0.243195

The 21-th FMG cycle:

The maximum norm of residuals after 21 times FMG cycle=3.23198

The 21-th residual reduction rate is about 0.339027

The maximum norm of error after 21 times FMG cycle=0.164844

The 22-th FMG cycle:

The maximum norm of residuals after 22 times FMG cycle=2.15403

The 22-th residual reduction rate is about 0.333524

The maximum norm of error after 22 times FMG cycle=0.11266

The 23-th FMG cycle:

The maximum norm of residuals after 23 times FMG cycle=1.39649

The 23-th residual reduction rate is about 0.351686

The maximum norm of error after 23 times FMG cycle=0.0782011

The 24-th FMG cycle:

The maximum norm of residuals after 24 times FMG cycle=0.859944

The 24-th residual reduction rate is about 0.384211

The maximum norm of error after 24 times FMG cycle=0.0555559

The 25-th FMG cycle:

The maximum norm of residuals after 25 times FMG cycle=0.555429

The 25-th residual reduction rate is about 0.35411

The maximum norm of error after 25 times FMG cycle=0.0408725

The 26-th FMG cycle:

The maximum norm of residuals after 26 times FMG cycle=0.560538

The 26-th residual reduction rate is about -0.00919753

The maximum norm of error after 26 times FMG cycle=0.0309848

The 27-th FMG cycle:

The maximum norm of residuals after 27 times FMG cycle=0.530723

The 27-th residual reduction rate is about 0.0531902

The maximum norm of error after 27 times FMG cycle=0.0257917

The 28-th FMG cycle:

The maximum norm of residuals after 28 times FMG cycle=0.479883

The 28-th residual reduction rate is about 0.0957944

The maximum norm of error after 28 times FMG cycle=0.0206931

The 29-th FMG cycle:

The maximum norm of residuals after 29 times FMG cycle=0.410502

The 29-th residual reduction rate is about 0.144577

The maximum norm of error after 29 times FMG cycle=0.0160805

The 30-th FMG cycle:

The maximum norm of residuals after 30 times FMG cycle=0.340606

The 30-th residual reduction rate is about 0.170271

The maximum norm of error after 30 times FMG cycle=0.0122016

The 31-th FMG cycle:

The maximum norm of residuals after 31 times FMG cycle=0.271052

The 31-th residual reduction rate is about 0.204205

The maximum norm of error after 31 times FMG cycle=0.0090992

The 32-th FMG cycle:

The maximum norm of residuals after 32 times FMG cycle=0.208122

The 32-th residual reduction rate is about 0.232172

The maximum norm of error after 32 times FMG cycle=0.00673103

The 33-th FMG cycle:

The maximum norm of residuals after 33 times FMG cycle=0.154748

The 33-th residual reduction rate is about 0.256455

The maximum norm of error after 33 times FMG cycle=0.00497357

The 34-th FMG cycle:

The maximum norm of residuals after 34 times FMG cycle=0.111662

The 34-th residual reduction rate is about 0.278425

The maximum norm of error after 34 times FMG cycle=0.00369902

The 35-th FMG cycle:

The maximum norm of residuals after 35 times FMG cycle=0.0782729

The 35-th residual reduction rate is about 0.299021

The maximum norm of error after 35 times FMG cycle=0.00278519

The 36-th FMG cycle:

The maximum norm of residuals after 36 times FMG cycle=0.0548104

The 36-th residual reduction rate is about 0.299752

The maximum norm of error after 36 times FMG cycle=0.00213316

The 37-th FMG cycle:

The maximum norm of residuals after 37 times FMG cycle=0.0383077

The 37-th residual reduction rate is about 0.301086

The maximum norm of error after 37 times FMG cycle=0.00167522

The 38-th FMG cycle:

The maximum norm of residuals after 38 times FMG cycle=0.0262027

The 38-th residual reduction rate is about 0.315995

The maximum norm of error after 38 times FMG cycle=0.00137118

The 39-th FMG cycle:

The maximum norm of residuals after 39 times FMG cycle=0.0174941

The 39-th residual reduction rate is about 0.332353

The maximum norm of error after 39 times FMG cycle=0.00114408

The 40-th FMG cycle:

The maximum norm of residuals after 40 times FMG cycle=0.0119594

The 40-th residual reduction rate is about 0.316377

The maximum norm of error after 40 times FMG cycle=0.000949278

The 41-th FMG cycle:

The maximum norm of residuals after 41 times FMG cycle=0.00816584

The 41-th residual reduction rate is about 0.317202

The maximum norm of error after 41 times FMG cycle=0.000774363

The 42-th FMG cycle:

The maximum norm of residuals after 42 times FMG cycle=0.00558914

The 42-th residual reduction rate is about 0.315546

The maximum norm of error after 42 times FMG cycle=0.000615494

The 43-th FMG cycle:

The maximum norm of residuals after 43 times FMG cycle=0.0044228

The 43-th residual reduction rate is about 0.20868

The maximum norm of error after 43 times FMG cycle=0.000474179

The 44-th FMG cycle:

The maximum norm of residuals after 44 times FMG cycle=0.00343953

The 44-th residual reduction rate is about 0.222318

The maximum norm of error after 44 times FMG cycle=0.000353099

The 45-th FMG cycle:

The maximum norm of residuals after 45 times FMG cycle=0.00257475

The 45-th residual reduction rate is about 0.251424

The maximum norm of error after 45 times FMG cycle=0.000253147

The 46-th FMG cycle:

The maximum norm of residuals after 46 times FMG cycle=0.00185533

The 46-th residual reduction rate is about 0.279412

The maximum norm of error after 46 times FMG cycle=0.000173917

The 47-th FMG cycle:

The maximum norm of residuals after 47 times FMG cycle=0.0012845

The 47-th residual reduction rate is about 0.30767

The maximum norm of error after 47 times FMG cycle=0.00011352

The 48-th FMG cycle:

The maximum norm of residuals after 48 times FMG cycle=0.000850552

The 48-th residual reduction rate is about 0.337836

The maximum norm of error after 48 times FMG cycle=6.93099e-05

The 49-th FMG cycle:

The maximum norm of residuals after 49 times FMG cycle=0.00053391

The 49-th residual reduction rate is about 0.372278

The maximum norm of error after 49 times FMG cycle=3.83782e-05

The 50-th FMG cycle:

The maximum norm of residuals after 50 times FMG cycle=0.000461629

The 50-th residual reduction rate is about 0.13538

The maximum norm of error after 50 times FMG cycle=1.78118e-05

The 51-th FMG cycle:

The maximum norm of residuals after 51 times FMG cycle=0.000404172

The 51-th residual reduction rate is about 0.124466

The maximum norm of error after 51 times FMG cycle=5.64692e-06

The 52-th FMG cycle:

The maximum norm of residuals after 52 times FMG cycle=0.000338193

The 52-th residual reduction rate is about 0.163245

The maximum norm of error after 52 times FMG cycle=7.99112e-06

The 53-th FMG cycle:

The maximum norm of residuals after 53 times FMG cycle=0.000278036

The 53-th residual reduction rate is about 0.177876

The maximum norm of error after 53 times FMG cycle=8.89134e-06

The 54-th FMG cycle:

The maximum norm of residuals after 54 times FMG cycle=0.000224853

The 54-th residual reduction rate is about 0.191282

The maximum norm of error after 54 times FMG cycle=8.69386e-06

The 55-th FMG cycle:

The maximum norm of residuals after 55 times FMG cycle=0.000175291

The 55-th residual reduction rate is about 0.220422

The maximum norm of error after 55 times FMG cycle=7.8408e-06

The 56-th FMG cycle:

The maximum norm of residuals after 56 times FMG cycle=0.000132218

The 56-th residual reduction rate is about 0.245721

The maximum norm of error after 56 times FMG cycle=6.69774e-06

The 57-th FMG cycle:

The maximum norm of residuals after 57 times FMG cycle=9.66643e-05

The 57-th residual reduction rate is about 0.268902

The maximum norm of error after 57 times FMG cycle=5.48227e-06

The 58-th FMG cycle:

The maximum norm of residuals after 58 times FMG cycle=7.01557e-05

The 58-th residual reduction rate is about 0.274234

The maximum norm of error after 58 times FMG cycle=4.26771e-06

The 59-th FMG cycle:

The maximum norm of residuals after 59 times FMG cycle=4.9922e-05

The 59-th residual reduction rate is about 0.288411

The maximum norm of error after 59 times FMG cycle=3.17531e-06

The 60-th FMG cycle:

The maximum norm of residuals after 60 times FMG cycle=3.43091e-05

The 60-th residual reduction rate is about 0.312747

The maximum norm of error after 60 times FMG cycle=2.26501e-06

The 61-th FMG cycle:

The maximum norm of residuals after 61 times FMG cycle=2.27157e-05

The 61-th residual reduction rate is about 0.337909

The maximum norm of error after 61 times FMG cycle=1.54771e-06

The 62-th FMG cycle:

The maximum norm of residuals after 62 times FMG cycle=1.51824e-05

The 62-th residual reduction rate is about 0.331637

The maximum norm of error after 62 times FMG cycle=1.00954e-06

The 63-th FMG cycle:

The maximum norm of residuals after 63 times FMG cycle=9.93926e-06

The 63-th residual reduction rate is about 0.345342

The maximum norm of error after 63 times FMG cycle=6.22593e-07

The 64-th FMG cycle:

The maximum norm of residuals after 64 times FMG cycle=6.23695e-06

The 64-th residual reduction rate is about 0.372493

The maximum norm of error after 64 times FMG cycle=3.56535e-07

The 65-th FMG cycle:

The maximum norm of residuals after 65 times FMG cycle=3.76904e-06

The 65-th residual reduction rate is about 0.395693

The maximum norm of error after 65 times FMG cycle=1.82091e-07

The 66-th FMG cycle:

The maximum norm of residuals after 66 times FMG cycle=2.50433e-06

The 66-th residual reduction rate is about 0.335552

The maximum norm of error after 66 times FMG cycle=7.4645e-08

The 67-th FMG cycle:

The maximum norm of residuals after 67 times FMG cycle=2.17965e-06

The 67-th residual reduction rate is about 0.129647

The maximum norm of error after 67 times FMG cycle=3.91602e-08

The 68-th FMG cycle:

The maximum norm of residuals after 68 times FMG cycle=1.86974e-06

The 68-th residual reduction rate is about 0.142183

The maximum norm of error after 68 times FMG cycle=5.69729e-08

The 69-th FMG cycle:

The maximum norm of residuals after 69 times FMG cycle=1.55564e-06

The 69-th residual reduction rate is about 0.167991

The maximum norm of error after 69 times FMG cycle=6.04822e-08

The 70-th FMG cycle:

The maximum norm of residuals after 70 times FMG cycle=1.25352e-06

The 70-th residual reduction rate is about 0.194213

The maximum norm of error after 70 times FMG cycle=5.6029e-08

The 71-th FMG cycle:

The maximum norm of residuals after 71 times FMG cycle=1.00159e-06

The 71-th residual reduction rate is about 0.200979

The maximum norm of error after 71 times FMG cycle=4.78227e-08

The 72-th FMG cycle:

The maximum norm of residuals after 72 times FMG cycle=7.72117e-07

The 72-th residual reduction rate is about 0.229106

The maximum norm of error after 72 times FMG cycle=3.85223e-08

The 73-th FMG cycle:

The maximum norm of residuals after 73 times FMG cycle=5.76525e-07

The 73-th residual reduction rate is about 0.253319

The maximum norm of error after 73 times FMG cycle=2.96049e-08

The 74-th FMG cycle:

The maximum norm of residuals after 74 times FMG cycle=4.22886e-07

The 74-th residual reduction rate is about 0.266492

The maximum norm of error after 74 times FMG cycle=2.18424e-08

The 75-th FMG cycle:

The maximum norm of residuals after 75 times FMG cycle=3.0794e-07

The 75-th residual reduction rate is about 0.271812

The maximum norm of error after 75 times FMG cycle=1.54945e-08

The 76-th FMG cycle:

The maximum norm of residuals after 76 times FMG cycle=2.18235e-07

The 76-th residual reduction rate is about 0.291308

The maximum norm of error after 76 times FMG cycle=1.05549e-08

The 77-th FMG cycle:

The maximum norm of residuals after 77 times FMG cycle=1.50358e-07

The 77-th residual reduction rate is about 0.311029

The maximum norm of error after 77 times FMG cycle=6.87017e-09

Obviously, the maximum norm of error has first-order convergence.

\subsection*{III-g n=129,RO=1,IO=1,cycletype=0}

The maximum norm of residuals and errors is shown below.

The 1-th V cycle:

The maximum norm of residuals after 1 times V cycle=1808.14

The 1-th residual reduction rate is about 0.976213

The maximum norm of error after 1 times V cycle=2.00139

The 2-th V cycle:

The maximum norm of residuals after 2 times V cycle=93.5514

The 2-th residual reduction rate is about 0.948261

The maximum norm of error after 2 times V cycle=1.84824

The 3-th V cycle:

The maximum norm of residuals after 3 times V cycle=5.95189

The 3-th residual reduction rate is about 0.936378

The maximum norm of error after 3 times V cycle=0.106475

The 4-th V cycle:

The maximum norm of residuals after 4 times V cycle=0.280291

The 4-th residual reduction rate is about 0.952907

The maximum norm of error after 4 times V cycle=0.00297684

The 5-th V cycle:

The maximum norm of residuals after 5 times V cycle=0.022286

The 5-th residual reduction rate is about 0.92049

The maximum norm of error after 5 times V cycle=0.000120552

The 6-th V cycle:

The maximum norm of residuals after 6 times V cycle=0.000991306

The 6-th residual reduction rate is about 0.955519

The maximum norm of error after 6 times V cycle=1.26564e-05

The 7-th V cycle:

The maximum norm of residuals after 7 times V cycle=5.83458e-05

The 7-th residual reduction rate is about 0.941142

The maximum norm of error after 7 times V cycle=6.34066e-07

The 8-th V cycle:

The maximum norm of residuals after 8 times V cycle=5.20684e-06

The 8-th residual reduction rate is about 0.910759

The maximum norm of error after 8 times V cycle=3.13489e-08

The 9-th V cycle:

The maximum norm of residuals after 9 times V cycle=2.75543e-07

The 9-th residual reduction rate is about 0.947081

The maximum norm of error after 9 times V cycle=1.68075e-09

Obviously, the maximum norm of error has second-order convergence.

\subsection*{III-h n=129,RO=1,IO=1,cycletype=1}

The maximum norm of residuals and errors is shown below.

The 1-th FMG cycle:

The maximum norm of residuals after 1 times FMG cycle=3562.81

The 1-th residual reduction rate is about 0.953129

The maximum norm of error after 1 times FMG cycle=1.68595

The 2-th FMG cycle:

The maximum norm of residuals after 2 times FMG cycle=1353.13

The 2-th residual reduction rate is about 0.620206

The maximum norm of error after 2 times FMG cycle=2.58633

The 3-th FMG cycle:

The maximum norm of residuals after 3 times FMG cycle=617.661

The 3-th residual reduction rate is about 0.543533

The maximum norm of error after 3 times FMG cycle=3.13124

The 4-th FMG cycle:

The maximum norm of residuals after 4 times FMG cycle=319.394

The 4-th residual reduction rate is about 0.482897

The maximum norm of error after 4 times FMG cycle=1.83323

The 5-th FMG cycle:

The maximum norm of residuals after 5 times FMG cycle=149.147

The 5-th residual reduction rate is about 0.533031

The maximum norm of error after 5 times FMG cycle=1.68813

The 6-th FMG cycle:

The maximum norm of residuals after 6 times FMG cycle=73.9576

The 6-th residual reduction rate is about 0.50413

The maximum norm of error after 6 times FMG cycle=1.70963

The 7-th FMG cycle:

The maximum norm of residuals after 7 times FMG cycle=41.8795

The 7-th residual reduction rate is about 0.433737

The maximum norm of error after 7 times FMG cycle=1.54875

The 8-th FMG cycle:

The maximum norm of residuals after 8 times FMG cycle=22.9133

The 8-th residual reduction rate is about 0.452876

The maximum norm of error after 8 times FMG cycle=1.45551

The 9-th FMG cycle:

The maximum norm of residuals after 9 times FMG cycle=15.5088

The 9-th residual reduction rate is about 0.323153

The maximum norm of error after 9 times FMG cycle=1.21838

The 10-th FMG cycle:

The maximum norm of residuals after 10 times FMG cycle=10.7304

The 10-th residual reduction rate is about 0.308111

The maximum norm of error after 10 times FMG cycle=0.911835

The 11-th FMG cycle:

The maximum norm of residuals after 11 times FMG cycle=6.70116

The 11-th residual reduction rate is about 0.375495

The maximum norm of error after 11 times FMG cycle=0.63936

The 12-th FMG cycle:

The maximum norm of residuals after 12 times FMG cycle=3.8595

The 12-th residual reduction rate is about 0.424055

The maximum norm of error after 12 times FMG cycle=0.435986

The 13-th FMG cycle:

The maximum norm of residuals after 13 times FMG cycle=2.29784

The 13-th residual reduction rate is about 0.404626

The maximum norm of error after 13 times FMG cycle=0.295228

The 14-th FMG cycle:

The maximum norm of residuals after 14 times FMG cycle=1.34506

The 14-th residual reduction rate is about 0.414644

The maximum norm of error after 14 times FMG cycle=0.199453

The 15-th FMG cycle:

The maximum norm of residuals after 15 times FMG cycle=0.837552

The 15-th residual reduction rate is about 0.377312

The maximum norm of error after 15 times FMG cycle=0.133557

The 16-th FMG cycle:

The maximum norm of residuals after 16 times FMG cycle=0.634679

The 16-th residual reduction rate is about 0.242222

The maximum norm of error after 16 times FMG cycle=0.0875256

The 17-th FMG cycle:

The maximum norm of residuals after 17 times FMG cycle=0.436004

The 17-th residual reduction rate is about 0.313032

The maximum norm of error after 17 times FMG cycle=0.0550643

The 18-th FMG cycle:

The maximum norm of residuals after 18 times FMG cycle=0.278175

The 18-th residual reduction rate is about 0.361991

The maximum norm of error after 18 times FMG cycle=0.0329029

The 19-th FMG cycle:

The maximum norm of residuals after 19 times FMG cycle=0.166327

The 19-th residual reduction rate is about 0.402076

The maximum norm of error after 19 times FMG cycle=0.0185646

The 20-th FMG cycle:

The maximum norm of residuals after 20 times FMG cycle=0.0999524

The 20-th residual reduction rate is about 0.399062

The maximum norm of error after 20 times FMG cycle=0.00983946

The 21-th FMG cycle:

The maximum norm of residuals after 21 times FMG cycle=0.0566913

The 21-th residual reduction rate is about 0.432817

The maximum norm of error after 21 times FMG cycle=0.00485551

The 22-th FMG cycle:

The maximum norm of residuals after 22 times FMG cycle=0.0304458

The 22-th residual reduction rate is about 0.462954

The maximum norm of error after 22 times FMG cycle=0.00219266

The 23-th FMG cycle:

The maximum norm of residuals after 23 times FMG cycle=0.0155597

The 23-th residual reduction rate is about 0.488938

The maximum norm of error after 23 times FMG cycle=0.000871924

The 24-th FMG cycle:

The maximum norm of residuals after 24 times FMG cycle=0.00780317

The 24-th residual reduction rate is about 0.498501

The maximum norm of error after 24 times FMG cycle=0.000276044

The 25-th FMG cycle:

The maximum norm of residuals after 25 times FMG cycle=0.00370947

The 25-th residual reduction rate is about 0.52462

The maximum norm of error after 25 times FMG cycle=8.53701e-05

The 26-th FMG cycle:

The maximum norm of residuals after 26 times FMG cycle=0.00172066

The 26-th residual reduction rate is about 0.536145

The maximum norm of error after 26 times FMG cycle=9.60042e-05

The 27-th FMG cycle:

The maximum norm of residuals after 27 times FMG cycle=0.000759048

The 27-th residual reduction rate is about 0.558861

The maximum norm of error after 27 times FMG cycle=7.90882e-05

The 28-th FMG cycle:


The maximum norm of residuals after 28 times FMG cycle=0.000412884

The 28-th residual reduction rate is about 0.45605

The maximum norm of error after 28 times FMG cycle=5.58652e-05

The 29-th FMG cycle:

The maximum norm of residuals after 29 times FMG cycle=0.000284729

The 29-th residual reduction rate is about 0.31039

The maximum norm of error after 29 times FMG cycle=3.58216e-05

The 30-th FMG cycle:

The maximum norm of residuals after 30 times FMG cycle=0.000175664

The 30-th residual reduction rate is about 0.383048

The maximum norm of error after 30 times FMG cycle=2.13731e-05

The 31-th FMG cycle:

The maximum norm of residuals after 31 times FMG cycle=0.000104478

The 31-th residual reduction rate is about 0.405242

The maximum norm of error after 31 times FMG cycle=1.20389e-05

The 32-th FMG cycle:

The maximum norm of residuals after 32 times FMG cycle=6.15319e-05

The 32-th residual reduction rate is about 0.411052

The maximum norm of error after 32 times FMG cycle=6.45641e-06

The 33-th FMG cycle:

The maximum norm of residuals after 33 times FMG cycle=3.4304e-05

The 33-th residual reduction rate is about 0.4425

The maximum norm of error after 33 times FMG cycle=3.31148e-06

The 34-th FMG cycle:

The maximum norm of residuals after 34 times FMG cycle=1.81577e-05

The 34-th residual reduction rate is about 0.470684

The maximum norm of error after 34 times FMG cycle=1.62709e-06

The 35-th FMG cycle:

The maximum norm of residuals after 35 times FMG cycle=9.24188e-06

The 35-th residual reduction rate is about 0.491021

The maximum norm of error after 35 times FMG cycle=7.64872e-07

The 36-th FMG cycle:

The maximum norm of residuals after 36 times FMG cycle=4.68332e-06

The 36-th residual reduction rate is about 0.49325

The maximum norm of error after 36 times FMG cycle=3.42192e-07

The 37-th FMG cycle:

The maximum norm of residuals after 37 times FMG cycle=2.27357e-06

The 37-th residual reduction rate is about 0.51454

The maximum norm of error after 37 times FMG cycle=1.43981e-07

The 38-th FMG cycle:

The maximum norm of residuals after 38 times FMG cycle=1.06382e-06

The 38-th residual reduction rate is about 0.532091

The maximum norm of error after 38 times FMG cycle=5.55207e-08

The 39-th FMG cycle:

The maximum norm of residuals after 39 times FMG cycle=4.9332e-07

The 39-th residual reduction rate is about 0.536276

The maximum norm of error after 39 times FMG cycle=1.84368e-08

The 40-th FMG cycle:

The maximum norm of residuals after 40 times FMG cycle=2.12878e-07

The 40-th residual reduction rate is about 0.568479

The maximum norm of error after 40 times FMG cycle=4.23423e-09

Obviously, the maximum norm of error has first-order convergence.

\subsection*{III-i n=257,RO=0,IO=0,cycletype=0}

The maximum norm of residuals and errors is shown below.

The 1-th V cycle:

The maximum norm of residuals after 1 times V cycle=4793.82

The 1-th residual reduction rate is about 0.984234

The maximum norm of error after 1 times V cycle=2.28441

The 2-th V cycle:

The maximum norm of residuals after 2 times V cycle=82.9015

The 2-th residual reduction rate is about 0.982707

The maximum norm of error after 2 times V cycle=0.129204

The 3-th V cycle:

The maximum norm of residuals after 3 times V cycle=1.78501

The 3-th residual reduction rate is about 0.978468

The maximum norm of error after 3 times V cycle=0.00433764

The 4-th V cycle:

The maximum norm of residuals after 4 times V cycle=0.0488573

The 4-th residual reduction rate is about 0.972629

The maximum norm of error after 4 times V cycle=0.00015945

The 5-th V cycle:

The maximum norm of residuals after 5 times V cycle=0.00164046

The 5-th residual reduction rate is about 0.966423

The maximum norm of error after 5 times V cycle=5.74951e-06

The 6-th V cycle:

The maximum norm of residuals after 6 times V cycle=4.99584e-05

The 6-th residual reduction rate is about 0.969546

The maximum norm of error after 6 times V cycle=2.0595e-07

The 7-th V cycle:

The maximum norm of residuals after 7 times V cycle=1.69296e-06

The 7-th residual reduction rate is about 0.966113

The maximum norm of error after 7 times V cycle=7.17657e-09

Obviously, the maximum norm of error has second-order convergence.

\subsection*{III-j n=257,RO=0,IO=0,cycletype=1}

The maximum norm of residuals and errors is shown below.

The 1-th FMG cycle:
 
The maximum norm of residuals after 1 times FMG cycle=8490.94

The 1-th residual reduction rate is about 0.972074

The maximum norm of error after 1 times FMG cycle=2.75377

The 2-th FMG cycle:
 
The maximum norm of residuals after 2 times FMG cycle=1274.56

The 2-th residual reduction rate is about 0.849892

The maximum norm of error after 2 times FMG cycle=0.565102

The 3-th FMG cycle:
 
The maximum norm of residuals after 3 times FMG cycle=296.376

The 3-th residual reduction rate is about 0.767469

The maximum norm of error after 3 times FMG cycle=0.180415

The 4-th FMG cycle:
 
The maximum norm of residuals after 4 times FMG cycle=90.3604

The 4-th residual reduction rate is about 0.695115

The maximum norm of error after 4 times FMG cycle=0.0656636

The 5-th FMG cycle:
 
The maximum norm of residuals after 5 times FMG cycle=28.2761

The 5-th residual reduction rate is about 0.687074

The maximum norm of error after 5 times FMG cycle=0.0239452

The 6-th FMG cycle:
 
The maximum norm of residuals after 6 times FMG cycle=9.03354

The 6-th residual reduction rate is about 0.680524

The maximum norm of error after 6 times FMG cycle=0.00872155

The 7-th FMG cycle:
 
The maximum norm of residuals after 7 times FMG cycle=2.93401

The 7-th residual reduction rate is about 0.675209

The maximum norm of error after 7 times FMG cycle=0.00316291

The 8-th FMG cycle:
 
The maximum norm of residuals after 8 times FMG cycle=0.965663

The 8-th residual reduction rate is about 0.670873

The maximum norm of error after 8 times FMG cycle=0.00114212

The 9-th FMG cycle:
 
The maximum norm of residuals after 9 times FMG cycle=0.321269

The 9-th residual reduction rate is about 0.667307

The maximum norm of error after 9 times FMG cycle=0.000410588

The 10-th FMG cycle:
 
The maximum norm of residuals after 10 times FMG cycle=0.107835

The 10-th residual reduction rate is about 0.664347

The maximum norm of error after 10 times FMG cycle=0.000146971

The 11-th FMG cycle:
 
The maximum norm of residuals after 11 times FMG cycle=0.036463

The 11-th residual reduction rate is about 0.661863

The maximum norm of error after 11 times FMG cycle=5.24162e-05

The 12-th FMG cycle:
 
The maximum norm of residuals after 12 times FMG cycle=0.0124063

The 12-th residual reduction rate is about 0.659756

The maximum norm of error after 12 times FMG cycle=1.86377e-05

The 13-th FMG cycle:
 
The maximum norm of residuals after 13 times FMG cycle=0.00424362

The 13-th residual reduction rate is about 0.657947

The maximum norm of error after 13 times FMG cycle=6.61146e-06

The 14-th FMG cycle:
 
The maximum norm of residuals after 14 times FMG cycle=0.0014582

The 14-th residual reduction rate is about 0.656378

The maximum norm of error after 14 times FMG cycle=2.34176e-06

The 15-th FMG cycle:
 
The maximum norm of residuals after 15 times FMG cycle=0.000503079

The 15-th residual reduction rate is about 0.655001

The maximum norm of error after 15 times FMG cycle=8.28988e-07

The 16-th FMG cycle:
 
The maximum norm of residuals after 16 times FMG cycle=0.000174176

The 16-th residual reduction rate is about 0.653779

The maximum norm of error after 16 times FMG cycle=2.93328e-07

The 17-th FMG cycle:
 
The maximum norm of residuals after 17 times FMG cycle=6.09832e-05

The 17-th residual reduction rate is about 0.649877

The maximum norm of error after 17 times FMG cycle=1.03792e-07

The 18-th FMG cycle:
 
The maximum norm of residuals after 18 times FMG cycle=2.14346e-05

The 18-th residual reduction rate is about 0.648516

The maximum norm of error after 18 times FMG cycle=3.67417e-08

The 19-th FMG cycle:
 
The maximum norm of residuals after 19 times FMG cycle=7.54672e-06

The 19-th residual reduction rate is about 0.647919

The maximum norm of error after 19 times FMG cycle=1.30163e-08

The 20-th FMG cycle:
 
The maximum norm of residuals after 20 times FMG cycle=2.66133e-06

The 20-th residual reduction rate is about 0.647353

The maximum norm of error after 20 times FMG cycle=4.61587e-09

Obviously, the maximum norm of error has first-order convergence.

\subsection*{III-k n=257,RO=0,IO=1,cycletype=0}

The maximum norm of residuals and errors is shown below.

The 1-th V cycle:

The maximum norm of residuals after 1 times V cycle=2848.51

The 1-th residual reduction rate is about 0.990632

The maximum norm of error after 1 times V cycle=2.3369

The 2-th V cycle:

The maximum norm of residuals after 2 times V cycle=64.6177

The 2-th residual reduction rate is about 0.977315

The maximum norm of error after 2 times V cycle=0.0270636

The 3-th V cycle:

The maximum norm of residuals after 3 times V cycle=0.689226

The 3-th residual reduction rate is about 0.989334

The maximum norm of error after 3 times V cycle=0.000985509

The 4-th V cycle:

The maximum norm of residuals after 4 times V cycle=0.0169241

The 4-th residual reduction rate is about 0.975445

The maximum norm of error after 4 times V cycle=1.67921e-05

The 5-th V cycle:

The maximum norm of residuals after 5 times V cycle=0.000344484

The 5-th residual reduction rate is about 0.979645

The maximum norm of error after 5 times V cycle=3.99336e-07

The 6-th V cycle:

The maximum norm of residuals after 6 times V cycle=7.2588e-06

The 6-th residual reduction rate is about 0.978929

The maximum norm of error after 6 times V cycle=1.13115e-08

The 7-th V cycle:

The maximum norm of residuals after 7 times V cycle=1.71201e-07

The 7-th residual reduction rate is about 0.976415

The maximum norm of error after 7 times V cycle=1.90867e-10

Obviously, the maximum norm of error has second-order convergence.

\subsection*{III-l n=257,RO=0,IO=1,cycletype=1}

The maximum norm of residuals and errors is shown below.

The 1-th FMG cycle:
 
The maximum norm of residuals after 1 times FMG cycle=12536.4

The 1-th residual reduction rate is about 0.958769

The maximum norm of error after 1 times FMG cycle=3.02221

The 2-th FMG cycle:
 
The maximum norm of residuals after 2 times FMG cycle=2926.53

The 2-th residual reduction rate is about 0.766558

The maximum norm of error after 2 times FMG cycle=0.945154

The 3-th FMG cycle:
 
The maximum norm of residuals after 3 times FMG cycle=755.458

The 3-th residual reduction rate is about 0.741859

The maximum norm of error after 3 times FMG cycle=0.32861

The 4-th FMG cycle:
 
The maximum norm of residuals after 4 times FMG cycle=230.181

The 4-th residual reduction rate is about 0.695309

The maximum norm of error after 4 times FMG cycle=0.133969

The 5-th FMG cycle:
 
The maximum norm of residuals after 5 times FMG cycle=83.4439

The 5-th residual reduction rate is about 0.637486

The maximum norm of error after 5 times FMG cycle=0.0602193

The 6-th FMG cycle:
 
The maximum norm of residuals after 6 times FMG cycle=31.5265

The 6-th residual reduction rate is about 0.622184

The maximum norm of error after 6 times FMG cycle=0.0270549

The 7-th FMG cycle:
 
The maximum norm of residuals after 7 times FMG cycle=12.6073

The 7-th residual reduction rate is about 0.600104

The maximum norm of error after 7 times FMG cycle=0.0121457

The 8-th FMG cycle:
 
The maximum norm of residuals after 8 times FMG cycle=5.12411

The 8-th residual reduction rate is about 0.59356

The maximum norm of error after 8 times FMG cycle=0.0054471

The 9-th FMG cycle:
 
The maximum norm of residuals after 9 times FMG cycle=2.11036

The 9-th residual reduction rate is about 0.588151

The maximum norm of error after 9 times FMG cycle=0.00244051

The 10-th FMG cycle:
 
The maximum norm of residuals after 10 times FMG cycle=0.878559

The 10-th residual reduction rate is about 0.583692

The maximum norm of error after 10 times FMG cycle=0.00109416

The 11-th FMG cycle:
 
The maximum norm of residuals after 11 times FMG cycle=0.368988

The 11-th residual reduction rate is about 0.580008

The maximum norm of error after 11 times FMG cycle=0.000490883

The 12-th FMG cycle:
 
The maximum norm of residuals after 12 times FMG cycle=0.156102

The 12-th residual reduction rate is about 0.576945

The maximum norm of error after 12 times FMG cycle=0.000220573

The 13-th FMG cycle:
 
The maximum norm of residuals after 13 times FMG cycle=0.0664402

The 13-th residual reduction rate is about 0.574379

The maximum norm of error after 13 times FMG cycle=9.94487e-05

The 14-th FMG cycle:
 
The maximum norm of residuals after 14 times FMG cycle=0.0284224

The 14-th residual reduction rate is about 0.572211

The maximum norm of error after 14 times FMG cycle=4.49797e-05

The 15-th FMG cycle:
 
The maximum norm of residuals after 15 times FMG cycle=0.0122113

The 15-th residual reduction rate is about 0.570362

The maximum norm of error after 15 times FMG cycle=2.04437e-05

The 16-th FMG cycle:
 
The maximum norm of residuals after 16 times FMG cycle=0.00526588

The 16-th residual reduction rate is about 0.568772

The maximum norm of error after 16 times FMG cycle=9.34233e-06

The 17-th FMG cycle:
 
The maximum norm of residuals after 17 times FMG cycle=0.00227807

The 17-th residual reduction rate is about 0.567391

The maximum norm of error after 17 times FMG cycle=4.29907e-06

The 18-th FMG cycle:
 
The maximum norm of residuals after 18 times FMG cycle=0.000988274

The 18-th residual reduction rate is about 0.566178

The maximum norm of error after 18 times FMG cycle=1.99326e-06

The 19-th FMG cycle:
 
The maximum norm of residuals after 19 times FMG cycle=0.0004298

The 19-th residual reduction rate is about 0.5651

The maximum norm of error after 19 times FMG cycle=9.32681e-07

The 20-th FMG cycle:
 
The maximum norm of residuals after 20 times FMG cycle=0.000187339

The 20-th residual reduction rate is about 0.564126

The maximum norm of error after 20 times FMG cycle=4.41919e-07

The 21-th FMG cycle:
 
The maximum norm of residuals after 21 times FMG cycle=8.18238e-05

The 21-th residual reduction rate is about 0.563231

The maximum norm of error after 21 times FMG cycle=2.121e-07

The 22-th FMG cycle:
 
The maximum norm of residuals after 22 times FMG cycle=3.58069e-05

The 22-th residual reduction rate is about 0.56239

The maximum norm of error after 22 times FMG cycle=1.02165e-07

The 23-th FMG cycle:
 
The maximum norm of residuals after 23 times FMG cycle=1.56984e-05

The 23-th residual reduction rate is about 0.561583

The maximum norm of error after 23 times FMG cycle=4.9187e-08

The 24-th FMG cycle:
 
The maximum norm of residuals after 24 times FMG cycle=6.89484e-06

The 24-th residual reduction rate is about 0.560793

The maximum norm of error after 24 times FMG cycle=2.36373e-08

The 25-th FMG cycle:
 
The maximum norm of residuals after 25 times FMG cycle=3.03376e-06

The 25-th residual reduction rate is about 0.559996

The maximum norm of error after 25 times FMG cycle=1.13293e-08

The 26-th FMG cycle:
 
The maximum norm of residuals after 26 times FMG cycle=1.33732e-06

The 26-th residual reduction rate is about 0.559188

The maximum norm of error after 26 times FMG cycle=5.41259e-09

Obviously, the maximum norm of error has first-order convergence.

\subsection*{III-m n=257,RO=1,IO=0,cycletype=0}

The maximum norm of residuals and errors is shown below.

The 1-th V cycle:

The maximum norm of residuals after 1 times V cycle=9752.93

The 1-th residual reduction rate is about 0.967924

The maximum norm of error after 1 times V cycle=1.9626

The 2-th V cycle:

The maximum norm of residuals after 2 times V cycle=669.336

The 2-th residual reduction rate is about 0.931371

The maximum norm of error after 2 times V cycle=1.92167

The 3-th V cycle:

The maximum norm of residuals after 3 times V cycle=52.2967

The 3-th residual reduction rate is about 0.921868

The maximum norm of error after 3 times V cycle=0.0630892

The 4-th V cycle:

The maximum norm of residuals after 4 times V cycle=5.28162

The 4-th residual reduction rate is about 0.899007

The maximum norm of error after 4 times V cycle=0.0464426

The 5-th V cycle:

The maximum norm of residuals after 5 times V cycle=0.449093

The 5-th residual reduction rate is about 0.914971

The maximum norm of error after 5 times V cycle=0.00206279

The 6-th V cycle:

The maximum norm of residuals after 6 times V cycle=0.0471542

The 6-th residual reduction rate is about 0.895001

The maximum norm of error after 6 times V cycle=0.000798353

The 7-th V cycle:

The maximum norm of residuals after 7 times V cycle=0.00478472

The 7-th residual reduction rate is about 0.898531

The maximum norm of error after 7 times V cycle=3.78189e-05

The 8-th V cycle:

The maximum norm of residuals after 8 times V cycle=0.000519025

The 8-th residual reduction rate is about 0.891524

The maximum norm of error after 8 times V cycle=1.23949e-05

The 9-th V cycle:

The maximum norm of residuals after 9 times V cycle=4.57521e-05

The 9-th residual reduction rate is about 0.91185

The maximum norm of error after 9 times V cycle=6.74149e-07

The 10-th V cycle:

The maximum norm of residuals after 10 times V cycle=5.66479e-06

The 10-th residual reduction rate is about 0.876185

The maximum norm of error after 10 times V cycle=1.85071e-07

The 11-th V cycle:

The maximum norm of residuals after 11 times V cycle=5.34794e-07

The 11-th residual reduction rate is about 0.905593

The maximum norm of error after 11 times V cycle=8.12368e-09

Obviously, the maximum norm of error has second-order convergence.

\subsection*{III-n n=257,RO=1,IO=0,cycletype=1}

The maximum norm of residuals and errors is shown below.

The 1-th FMG cycle:
 
The maximum norm of residuals after 1 times FMG cycle=14252.2

The 1-th residual reduction rate is about 0.953126

The maximum norm of error after 1 times FMG cycle=1.68571

The 2-th FMG cycle:
 
The maximum norm of residuals after 2 times FMG cycle=5007.44

The 2-th residual reduction rate is about 0.648656

The maximum norm of error after 2 times FMG cycle=2.41456

The 3-th FMG cycle:
 
The maximum norm of residuals after 3 times FMG cycle=2736.88

The 3-th residual reduction rate is about 0.453438

The maximum norm of error after 3 times FMG cycle=2.99713

The 4-th FMG cycle:
 
The maximum norm of residuals after 4 times FMG cycle=1843.14

The 4-th residual reduction rate is about 0.326553

The maximum norm of error after 4 times FMG cycle=4.30141

The 5-th FMG cycle:
 
The maximum norm of residuals after 5 times FMG cycle=1127.15

The 5-th residual reduction rate is about 0.38846

The maximum norm of error after 5 times FMG cycle=6.14213

The 6-th FMG cycle:
 
The maximum norm of residuals after 6 times FMG cycle=984.331

The 6-th residual reduction rate is about 0.126711

The maximum norm of error after 6 times FMG cycle=7.15709

The 7-th FMG cycle:
 
The maximum norm of residuals after 7 times FMG cycle=756.344

The 7-th residual reduction rate is about 0.231617

The maximum norm of error after 7 times FMG cycle=6.99388

The 8-th FMG cycle:
 
The maximum norm of residuals after 8 times FMG cycle=532.701

The 8-th residual reduction rate is about 0.295689

The maximum norm of error after 8 times FMG cycle=5.54558

The 9-th FMG cycle:
 
The maximum norm of residuals after 9 times FMG cycle=352.714

The 9-th residual reduction rate is about 0.337876

The maximum norm of error after 9 times FMG cycle=3.61237

The 10-th FMG cycle:
 
The maximum norm of residuals after 10 times FMG cycle=229.61

The 10-th residual reduction rate is about 0.349021

The maximum norm of error after 10 times FMG cycle=1.82268

The 11-th FMG cycle:
 
The maximum norm of residuals after 11 times FMG cycle=169.893

The 11-th residual reduction rate is about 0.26008

The maximum norm of error after 11 times FMG cycle=2.11924

The 12-th FMG cycle:
 
The maximum norm of residuals after 12 times FMG cycle=142.559

The 12-th residual reduction rate is about 0.160886

The maximum norm of error after 12 times FMG cycle=2.53128

The 13-th FMG cycle:
 
The maximum norm of residuals after 13 times FMG cycle=132.905

The 13-th residual reduction rate is about 0.0677231

The maximum norm of error after 13 times FMG cycle=2.55889

The 14-th FMG cycle:
 
The maximum norm of residuals after 14 times FMG cycle=112.901

The 14-th residual reduction rate is about 0.150516

The maximum norm of error after 14 times FMG cycle=2.33626

The 15-th FMG cycle:
 
The maximum norm of residuals after 15 times FMG cycle=89.2784

The 15-th residual reduction rate is about 0.20923

The maximum norm of error after 15 times FMG cycle=1.99484

The 16-th FMG cycle:
 
The maximum norm of residuals after 16 times FMG cycle=66.6095

The 16-th residual reduction rate is about 0.253913

The maximum norm of error after 16 times FMG cycle=1.63373

The 17-th FMG cycle:
 
The maximum norm of residuals after 17 times FMG cycle=50.4562

The 17-th residual reduction rate is about 0.242508

The maximum norm of error after 17 times FMG cycle=1.3102

The 18-th FMG cycle:
 
The maximum norm of residuals after 18 times FMG cycle=38.7508

The 18-th residual reduction rate is about 0.231992

The maximum norm of error after 18 times FMG cycle=1.04622

The 19-th FMG cycle:
 
The maximum norm of residuals after 19 times FMG cycle=28.2767

The 19-th residual reduction rate is about 0.270293

The maximum norm of error after 19 times FMG cycle=0.903995

The 20-th FMG cycle:
 
The maximum norm of residuals after 20 times FMG cycle=19.6294

The 20-th residual reduction rate is about 0.30581

The maximum norm of error after 20 times FMG cycle=0.809479

The 21-th FMG cycle:
 
The maximum norm of residuals after 21 times FMG cycle=14.0415

The 21-th residual reduction rate is about 0.284671

The maximum norm of error after 21 times FMG cycle=0.700093

The 22-th FMG cycle:
 
The maximum norm of residuals after 22 times FMG cycle=10.6436

The 22-th residual reduction rate is about 0.241991

The maximum norm of error after 22 times FMG cycle=0.581693

The 23-th FMG cycle:
 
The maximum norm of residuals after 23 times FMG cycle=7.7909

The 23-th residual reduction rate is about 0.268018

The maximum norm of error after 23 times FMG cycle=0.463606

The 24-th FMG cycle:
 
The maximum norm of residuals after 24 times FMG cycle=5.50255

The 24-th residual reduction rate is about 0.293721

The maximum norm of error after 24 times FMG cycle=0.354119

The 25-th FMG cycle:
 
The maximum norm of residuals after 25 times FMG cycle=4.18094

The 25-th residual reduction rate is about 0.240182

The maximum norm of error after 25 times FMG cycle=0.259067

The 26-th FMG cycle:
 
The maximum norm of residuals after 26 times FMG cycle=3.30818

The 26-th residual reduction rate is about 0.208746

The maximum norm of error after 26 times FMG cycle=0.181609

The 27-th FMG cycle:
 
The maximum norm of residuals after 27 times FMG cycle=2.54861

The 27-th residual reduction rate is about 0.229604

The maximum norm of error after 27 times FMG cycle=0.122094

The 28-th FMG cycle:
 
The maximum norm of residuals after 28 times FMG cycle=2.02465

The 28-th residual reduction rate is about 0.205588

The maximum norm of error after 28 times FMG cycle=0.0787843

The 29-th FMG cycle:
 
The maximum norm of residuals after 29 times FMG cycle=1.67318

The 29-th residual reduction rate is about 0.173594

The maximum norm of error after 29 times FMG cycle=0.0487267

The 30-th FMG cycle:
 
The maximum norm of residuals after 30 times FMG cycle=1.33258

The 30-th residual reduction rate is about 0.203562

The maximum norm of error after 30 times FMG cycle=0.0287549

The 31-th FMG cycle:
 
The maximum norm of residuals after 31 times FMG cycle=1.02552

The 31-th residual reduction rate is about 0.23043

The maximum norm of error after 31 times FMG cycle=0.0175745

The 32-th FMG cycle:
 
The maximum norm of residuals after 32 times FMG cycle=0.762841

The 32-th residual reduction rate is about 0.25614

The maximum norm of error after 32 times FMG cycle=0.0136871

The 33-th FMG cycle:
 
The maximum norm of residuals after 33 times FMG cycle=0.547559

The 33-th residual reduction rate is about 0.28221

The maximum norm of error after 33 times FMG cycle=0.0104902

The 34-th FMG cycle:
 
The maximum norm of residuals after 34 times FMG cycle=0.377732

The 34-th residual reduction rate is about 0.310154

The maximum norm of error after 34 times FMG cycle=0.00807653

The 35-th FMG cycle:
 
The maximum norm of residuals after 35 times FMG cycle=0.248577

The 35-th residual reduction rate is about 0.341921

The maximum norm of error after 35 times FMG cycle=0.00646819

The 36-th FMG cycle:
 
The maximum norm of residuals after 36 times FMG cycle=0.167943

The 36-th residual reduction rate is about 0.324382

The maximum norm of error after 36 times FMG cycle=0.005736

The 37-th FMG cycle:
 
The maximum norm of residuals after 37 times FMG cycle=0.146376

The 37-th residual reduction rate is about 0.128418

The maximum norm of error after 37 times FMG cycle=0.00530881

The 38-th FMG cycle:
 
The maximum norm of residuals after 38 times FMG cycle=0.123832

The 38-th residual reduction rate is about 0.154013

The maximum norm of error after 38 times FMG cycle=0.00490372

The 39-th FMG cycle:
 
The maximum norm of residuals after 39 times FMG cycle=0.102052

The 39-th residual reduction rate is about 0.175885

The maximum norm of error after 39 times FMG cycle=0.00444521

The 40-th FMG cycle:
 
The maximum norm of residuals after 40 times FMG cycle=0.0833217

The 40-th residual reduction rate is about 0.183537

The maximum norm of error after 40 times FMG cycle=0.00392825

The 41-th FMG cycle:
 
The maximum norm of residuals after 41 times FMG cycle=0.0664153

The 41-th residual reduction rate is about 0.202905

The maximum norm of error after 41 times FMG cycle=0.00336922

The 42-th FMG cycle:
 
The maximum norm of residuals after 42 times FMG cycle=0.0512996

The 42-th residual reduction rate is about 0.227594

The maximum norm of error after 42 times FMG cycle=0.00279443

The 43-th FMG cycle:
 
The maximum norm of residuals after 43 times FMG cycle=0.0383249

The 43-th residual reduction rate is about 0.252919

The maximum norm of error after 43 times FMG cycle=0.00223401

The 44-th FMG cycle:
 
The maximum norm of residuals after 44 times FMG cycle=0.0275982

The 44-th residual reduction rate is about 0.279888

The maximum norm of error after 44 times FMG cycle=0.0017138

The 45-th FMG cycle:
 
The maximum norm of residuals after 45 times FMG cycle=0.0190455

The 45-th residual reduction rate is about 0.309903

The maximum norm of error after 45 times FMG cycle=0.00125418

The 46-th FMG cycle:
 
The maximum norm of residuals after 46 times FMG cycle=0.0127673

The 46-th residual reduction rate is about 0.329641

The maximum norm of error after 46 times FMG cycle=0.00086688

The 47-th FMG cycle:
 
The maximum norm of residuals after 47 times FMG cycle=0.00838427

The 47-th residual reduction rate is about 0.3433

The maximum norm of error after 47 times FMG cycle=0.000555475

The 48-th FMG cycle:
 
The maximum norm of residuals after 48 times FMG cycle=0.00678867

The 48-th residual reduction rate is about 0.190309

The maximum norm of error after 48 times FMG cycle=0.000317257

The 49-th FMG cycle:
 
The maximum norm of residuals after 49 times FMG cycle=0.00566529

The 49-th residual reduction rate is about 0.165479

The maximum norm of error after 49 times FMG cycle=0.000144656

The 50-th FMG cycle:
 
The maximum norm of residuals after 50 times FMG cycle=0.00461091

The 50-th residual reduction rate is about 0.186112

The maximum norm of error after 50 times FMG cycle=2.73786e-05

The 51-th FMG cycle:
 
The maximum norm of residuals after 51 times FMG cycle=0.00366768

The 51-th residual reduction rate is about 0.204565

The maximum norm of error after 51 times FMG cycle=4.8705e-05

The 52-th FMG cycle:
 
The maximum norm of residuals after 52 times FMG cycle=0.00285551

The 52-th residual reduction rate is about 0.22144

The maximum norm of error after 52 times FMG cycle=8.62725e-05

The 53-th FMG cycle:
 
The maximum norm of residuals after 53 times FMG cycle=0.00217845

The 53-th residual reduction rate is about 0.237104

The maximum norm of error after 53 times FMG cycle=0.000102642

The 54-th FMG cycle:
 
The maximum norm of residuals after 54 times FMG cycle=0.00162996

The 54-th residual reduction rate is about 0.25178

The maximum norm of error after 54 times FMG cycle=0.000103648

The 55-th FMG cycle:
 
The maximum norm of residuals after 55 times FMG cycle=0.00119704

The 55-th residual reduction rate is about 0.265604

The maximum norm of error after 55 times FMG cycle=9.54355e-05

The 56-th FMG cycle:
 
The maximum norm of residuals after 56 times FMG cycle=0.00100277

The 56-th residual reduction rate is about 0.162289

The maximum norm of error after 56 times FMG cycle=8.25611e-05

The 57-th FMG cycle:
 
The maximum norm of residuals after 57 times FMG cycle=0.000841175

The 57-th residual reduction rate is about 0.161151

The maximum norm of error after 57 times FMG cycle=6.81371e-05

The 58-th FMG cycle:
 
The maximum norm of residuals after 58 times FMG cycle=0.000675489

The 58-th residual reduction rate is about 0.19697

The maximum norm of error after 58 times FMG cycle=5.41158e-05

The 59-th FMG cycle:
 
The maximum norm of residuals after 59 times FMG cycle=0.000522411

The 59-th residual reduction rate is about 0.226618

The maximum norm of error after 59 times FMG cycle=4.15851e-05

The 60-th FMG cycle:
 
The maximum norm of residuals after 60 times FMG cycle=0.000390348

The 60-th residual reduction rate is about 0.252795

The maximum norm of error after 60 times FMG cycle=3.1019e-05

The 61-th FMG cycle:
 
The maximum norm of residuals after 61 times FMG cycle=0.00028212

The 61-th residual reduction rate is about 0.277259

The maximum norm of error after 61 times FMG cycle=2.25003e-05

The 62-th FMG cycle:
 
The maximum norm of residuals after 62 times FMG cycle=0.00019866

The 62-th residual reduction rate is about 0.295831

The maximum norm of error after 62 times FMG cycle=1.58815e-05

The 63-th FMG cycle:
 
The maximum norm of residuals after 63 times FMG cycle=0.00013727

The 63-th residual reduction rate is about 0.309021

The maximum norm of error after 63 times FMG cycle=1.09014e-05

The 64-th FMG cycle:
 
The maximum norm of residuals after 64 times FMG cycle=9.14865e-05

The 64-th residual reduction rate is about 0.333529

The maximum norm of error after 64 times FMG cycle=7.26225e-06

The 65-th FMG cycle:
 
The maximum norm of residuals after 65 times FMG cycle=5.83869e-05

The 65-th residual reduction rate is about 0.361798

The maximum norm of error after 65 times FMG cycle=4.6753e-06

The 66-th FMG cycle:
 
The maximum norm of residuals after 66 times FMG cycle=3.52047e-05

The 66-th residual reduction rate is about 0.397044

The maximum norm of error after 66 times FMG cycle=2.88593e-06

The 67-th FMG cycle:
 
The maximum norm of residuals after 67 times FMG cycle=2.81036e-05

The 67-th residual reduction rate is about 0.20171

The maximum norm of error after 67 times FMG cycle=1.68402e-06

The 68-th FMG cycle:
 
The maximum norm of residuals after 68 times FMG cycle=2.34343e-05

The 68-th residual reduction rate is about 0.166146

The maximum norm of error after 68 times FMG cycle=9.03137e-07

The 69-th FMG cycle:
 
The maximum norm of residuals after 69 times FMG cycle=1.90411e-05

The 69-th residual reduction rate is about 0.187468

The maximum norm of error after 69 times FMG cycle=5.2237e-07

The 70-th FMG cycle:
 
The maximum norm of residuals after 70 times FMG cycle=1.53284e-05

The 70-th residual reduction rate is about 0.194982

The maximum norm of error after 70 times FMG cycle=3.0751e-07

The 71-th FMG cycle:
 
The maximum norm of residuals after 71 times FMG cycle=1.21617e-05

The 71-th residual reduction rate is about 0.206589

The maximum norm of error after 71 times FMG cycle=1.76092e-07

The 72-th FMG cycle:
 
The maximum norm of residuals after 72 times FMG cycle=9.48037e-06

The 72-th residual reduction rate is about 0.220475

The maximum norm of error after 72 times FMG cycle=1.47672e-07

The 73-th FMG cycle:
 
The maximum norm of residuals after 73 times FMG cycle=7.27782e-06

The 73-th residual reduction rate is about 0.232327

The maximum norm of error after 73 times FMG cycle=1.75109e-07

The 74-th FMG cycle:
 
The maximum norm of residuals after 74 times FMG cycle=5.46738e-06

The 74-th residual reduction rate is about 0.248761

The maximum norm of error after 74 times FMG cycle=1.73951e-07

The 75-th FMG cycle:
 
The maximum norm of residuals after 75 times FMG cycle=4.01723e-06

The 75-th residual reduction rate is about 0.265237

The maximum norm of error after 75 times FMG cycle=1.57727e-07

The 76-th FMG cycle:
 
The maximum norm of residuals after 76 times FMG cycle=2.89237e-06

The 76-th residual reduction rate is about 0.280009

The maximum norm of error after 76 times FMG cycle=1.3501e-07

The 77-th FMG cycle:
 
The maximum norm of residuals after 77 times FMG cycle=2.04279e-06

The 77-th residual reduction rate is about 0.293731

The maximum norm of error after 77 times FMG cycle=1.10875e-07

The 78-th FMG cycle:
 
The maximum norm of residuals after 78 times FMG cycle=1.40723e-06

The 78-th residual reduction rate is about 0.311123

The maximum norm of error after 78 times FMG cycle=8.81561e-08

The 79-th FMG cycle:
 
The maximum norm of residuals after 79 times FMG cycle=1.15902e-06

The 79-th residual reduction rate is about 0.176387

The maximum norm of error after 79 times FMG cycle=6.82335e-08

The 80-th FMG cycle:
 
The maximum norm of residuals after 80 times FMG cycle=9.63148e-07

The 80-th residual reduction rate is about 0.168996

The maximum norm of error after 80 times FMG cycle=5.15906e-08

The 81-th FMG cycle:
 
The maximum norm of residuals after 81 times FMG cycle=7.76359e-07

The 81-th residual reduction rate is about 0.193936

The maximum norm of error after 81 times FMG cycle=3.81845e-08

The 82-th FMG cycle:
 
The maximum norm of residuals after 82 times FMG cycle=6.091e-07

The 82-th residual reduction rate is about 0.215441

The maximum norm of error after 82 times FMG cycle=2.77043e-08

The 83-th FMG cycle:
 
The maximum norm of residuals after 83 times FMG cycle=4.66229e-07

The 83-th residual reduction rate is about 0.234561

The maximum norm of error after 83 times FMG cycle=1.97201e-08

The 84-th FMG cycle:
 
The maximum norm of residuals after 84 times FMG cycle=3.48737e-07

The 84-th residual reduction rate is about 0.252005

The maximum norm of error after 84 times FMG cycle=1.37753e-08

The 85-th FMG cycle:
 
The maximum norm of residuals after 85 times FMG cycle=2.55139e-07

The 85-th residual reduction rate is about 0.268392

The maximum norm of error after 85 times FMG cycle=9.44502e-09

Obviously, the maximum norm of error has the first order convergence.

\subsection*{III-o n=257,RO=1,IO=1,cycletype=0}

The maximum norm of residuals and errors is shown below.

The 1-th V cycle:

The maximum norm of residuals after 1 times V cycle=7232.47

The 1-th residual reduction rate is about 0.976213

The maximum norm of error after 1 times V cycle=1.99771

The 2-th V cycle:

The maximum norm of residuals after 2 times V cycle=374.183

The 2-th residual reduction rate is about 0.948263

The maximum norm of error after 2 times V cycle=2.05665

The 3-th V cycle:

The maximum norm of residuals after 3 times V cycle=23.8061

The 3-th residual reduction rate is about 0.936379

The maximum norm of error after 3 times V cycle=0.157859

The 4-th V cycle:

The maximum norm of residuals after 4 times V cycle=1.12114

The 4-th residual reduction rate is about 0.952905

The maximum norm of error after 4 times V cycle=0.00463523

The 5-th V cycle:

The maximum norm of residuals after 5 times V cycle=0.0891524

The 5-th residual reduction rate is about 0.92048

The maximum norm of error after 5 times V cycle=0.000130945

The 6-th V cycle:

The maximum norm of residuals after 6 times V cycle=0.00396532

The 6-th residual reduction rate is about 0.955522

The maximum norm of error after 6 times V cycle=1.67867e-05

The 7-th V cycle:

The maximum norm of residuals after 7 times V cycle=0.000233452

The 7-th residual reduction rate is about 0.941127

The maximum norm of error after 7 times V cycle=6.1677e-07

The 8-th V cycle:

The maximum norm of residuals after 8 times V cycle=2.08306e-05

The 8-th residual reduction rate is about 0.910771

The maximum norm of error after 8 times V cycle=1.01765e-07

The 9-th V cycle:

The maximum norm of residuals after 9 times V cycle=1.10149e-06

The 9-th residual reduction rate is about 0.947121

The maximum norm of error after 9 times V cycle=7.01944e-09

Obviously, the maximum norm of error has second-order convergence.

\subsection*{III-p n=257,RO=1,IO=1,cycletype=1}

The maximum norm of residuals and errors is shown below.

The 1-th FMG cycle:
 
The maximum norm of residuals after 1 times FMG cycle=14252.3

The 1-th residual reduction rate is about 0.953126

The maximum norm of error after 1 times FMG cycle=1.68573

The 2-th FMG cycle:
 
The maximum norm of residuals after 2 times FMG cycle=5413.11

The 2-th residual reduction rate is about 0.620194

The maximum norm of error after 2 times FMG cycle=2.58547

The 3-th FMG cycle:
 
The maximum norm of residuals after 3 times FMG cycle=2470.75

The 3-th residual reduction rate is about 0.543561

The maximum norm of error after 3 times FMG cycle=2.95311

The 4-th FMG cycle:
 
The maximum norm of residuals after 4 times FMG cycle=1277.52

The 4-th residual reduction rate is about 0.482945

The maximum norm of error after 4 times FMG cycle=3.89583

The 5-th FMG cycle:
 
The maximum norm of residuals after 5 times FMG cycle=596.557

The 5-th residual reduction rate is about 0.533034

The maximum norm of error after 5 times FMG cycle=4.74906

The 6-th FMG cycle:
 
The maximum norm of residuals after 6 times FMG cycle=296.552

The 6-th residual reduction rate is about 0.502894

The maximum norm of error after 6 times FMG cycle=4.4235

The 7-th FMG cycle:
 
The maximum norm of residuals after 7 times FMG cycle=167.831

The 7-th residual reduction rate is about 0.43406

The maximum norm of error after 7 times FMG cycle=3.43599

The 8-th FMG cycle:
 
The maximum norm of residuals after 8 times FMG cycle=91.5522

The 8-th residual reduction rate is about 0.454496

The maximum norm of error after 8 times FMG cycle=2.30998

The 9-th FMG cycle:
 
The maximum norm of residuals after 9 times FMG cycle=61.7338

The 9-th residual reduction rate is about 0.325699

The maximum norm of error after 9 times FMG cycle=1.46013

The 10-th FMG cycle:
 
The maximum norm of residuals after 10 times FMG cycle=42.1713

The 10-th residual reduction rate is about 0.316885

The maximum norm of error after 10 times FMG cycle=0.977989

The 11-th FMG cycle:
 
The maximum norm of residuals after 11 times FMG cycle=25.8994

The 11-th residual reduction rate is about 0.385851

The maximum norm of error after 11 times FMG cycle=0.660002

The 12-th FMG cycle:
 
The maximum norm of residuals after 12 times FMG cycle=14.574

The 12-th residual reduction rate is about 0.437286

The maximum norm of error after 12 times FMG cycle=0.442641

The 13-th FMG cycle:
 
The maximum norm of residuals after 13 times FMG cycle=8.38191

The 13-th residual reduction rate is about 0.424872

The maximum norm of error after 13 times FMG cycle=0.295234

The 14-th FMG cycle:
 
The maximum norm of residuals after 14 times FMG cycle=4.75264

The 14-th residual reduction rate is about 0.432988

The maximum norm of error after 14 times FMG cycle=0.194673

The 15-th FMG cycle:
 
The maximum norm of residuals after 15 times FMG cycle=3.05363

The 15-th residual reduction rate is about 0.357487

The maximum norm of error after 15 times FMG cycle=0.125048

The 16-th FMG cycle:
 
The maximum norm of residuals after 16 times FMG cycle=1.93244

The 16-th residual reduction rate is about 0.367166

The maximum norm of error after 16 times FMG cycle=0.0844388

The 17-th FMG cycle:
 
The maximum norm of residuals after 17 times FMG cycle=1.22701

The 17-th residual reduction rate is about 0.365045

The maximum norm of error after 17 times FMG cycle=0.0592223

The 18-th FMG cycle:
 
The maximum norm of residuals after 18 times FMG cycle=0.75129

The 18-th residual reduction rate is about 0.387708

The maximum norm of error after 18 times FMG cycle=0.0418295

The 19-th FMG cycle:
 
The maximum norm of residuals after 19 times FMG cycle=0.458413

The 19-th residual reduction rate is about 0.389833

The maximum norm of error after 19 times FMG cycle=0.0301185

The 20-th FMG cycle:
 
The maximum norm of residuals after 20 times FMG cycle=0.283185

The 20-th residual reduction rate is about 0.382249

The maximum norm of error after 20 times FMG cycle=0.0221463

The 21-th FMG cycle:
 
The maximum norm of residuals after 21 times FMG cycle=0.178754

The 21-th residual reduction rate is about 0.368774

The maximum norm of error after 21 times FMG cycle=0.0164919

The 22-th FMG cycle:
 
The maximum norm of residuals after 22 times FMG cycle=0.111013

The 22-th residual reduction rate is about 0.37896

The maximum norm of error after 22 times FMG cycle=0.0122556

The 23-th FMG cycle:
 
The maximum norm of residuals after 23 times FMG cycle=0.0678959

The 23-th residual reduction rate is about 0.388399

The maximum norm of error after 23 times FMG cycle=0.00896936

The 24-th FMG cycle:
 
The maximum norm of residuals after 24 times FMG cycle=0.0426671

The 24-th residual reduction rate is about 0.37158

The maximum norm of error after 24 times FMG cycle=0.00640146

The 25-th FMG cycle:
 
The maximum norm of residuals after 25 times FMG cycle=0.0266918

The 25-th residual reduction rate is about 0.374417

The maximum norm of error after 25 times FMG cycle=0.00443387

The 26-th FMG cycle:
 
The maximum norm of residuals after 26 times FMG cycle=0.018468

The 26-th residual reduction rate is about 0.3081

The maximum norm of error after 26 times FMG cycle=0.00297393

The 27-th FMG cycle:
 
The maximum norm of residuals after 27 times FMG cycle=0.0128679

The 27-th residual reduction rate is about 0.303234

The maximum norm of error after 27 times FMG cycle=0.00193023

The 28-th FMG cycle:
 
The maximum norm of residuals after 28 times FMG cycle=0.00852792

The 28-th residual reduction rate is about 0.337272

The maximum norm of error after 28 times FMG cycle=0.00121348

The 29-th FMG cycle:
 
The maximum norm of residuals after 29 times FMG cycle=0.00546235

The 29-th residual reduction rate is about 0.359475

The maximum norm of error after 29 times FMG cycle=0.00074081

The 30-th FMG cycle:
 
The maximum norm of residuals after 30 times FMG cycle=0.00347494

The 30-th residual reduction rate is about 0.363838

The maximum norm of error after 30 times FMG cycle=0.000440385

The 31-th FMG cycle:
 
The maximum norm of residuals after 31 times FMG cycle=0.00214795

The 31-th residual reduction rate is about 0.381874

The maximum norm of error after 31 times FMG cycle=0.000255624

The 32-th FMG cycle:
 
The maximum norm of residuals after 32 times FMG cycle=0.00130296

The 32-th residual reduction rate is about 0.393394

The maximum norm of error after 32 times FMG cycle=0.000145272

The 33-th FMG cycle:
 
The maximum norm of residuals after 33 times FMG cycle=0.000767053

The 33-th residual reduction rate is about 0.411299

The maximum norm of error after 33 times FMG cycle=8.10279e-05

The 34-th FMG cycle:
 
The maximum norm of residuals after 34 times FMG cycle=0.000439708

The 34-th residual reduction rate is about 0.426756

The maximum norm of error after 34 times FMG cycle=4.44586e-05

The 35-th FMG cycle:
 
The maximum norm of residuals after 35 times FMG cycle=0.000249894

The 35-th residual reduction rate is about 0.431683

The maximum norm of error after 35 times FMG cycle=2.40448e-05

The 36-th FMG cycle:
 
The maximum norm of residuals after 36 times FMG cycle=0.000141574

The 36-th residual reduction rate is about 0.433464

The maximum norm of error after 36 times FMG cycle=1.2838e-05

The 37-th FMG cycle:
 
The maximum norm of residuals after 37 times FMG cycle=7.89697e-05

The 37-th residual reduction rate is about 0.442201

The maximum norm of error after 37 times FMG cycle=6.77381e-06

The 38-th FMG cycle:
 
The maximum norm of residuals after 38 times FMG cycle=4.31654e-05

The 38-th residual reduction rate is about 0.453393

The maximum norm of error after 38 times FMG cycle=3.53336e-06

The 39-th FMG cycle:
 
The maximum norm of residuals after 39 times FMG cycle=2.31583e-05

The 39-th residual reduction rate is about 0.463498

The maximum norm of error after 39 times FMG cycle=1.82121e-06

The 40-th FMG cycle:
 
The maximum norm of residuals after 40 times FMG cycle=1.22742e-05

The 40-th residual reduction rate is about 0.469986

The maximum norm of error after 40 times FMG cycle=9.26179e-07

The 41-th FMG cycle:
 
The maximum norm of residuals after 41 times FMG cycle=6.49463e-06

The 41-th residual reduction rate is about 0.470872

The maximum norm of error after 41 times FMG cycle=4.63348e-07

The 42-th FMG cycle:
 
The maximum norm of residuals after 42 times FMG cycle=3.38522e-06

The 42-th residual reduction rate is about 0.478767

The maximum norm of error after 42 times FMG cycle=2.26905e-07

The 43-th FMG cycle:
 
The maximum norm of residuals after 43 times FMG cycle=1.74128e-06

The 43-th residual reduction rate is about 0.485623

The maximum norm of error after 43 times FMG cycle=1.07896e-07

The 44-th FMG cycle:
 
The maximum norm of residuals after 44 times FMG cycle=8.85344e-07

The 44-th residual reduction rate is about 0.491555

The maximum norm of error after 44 times FMG cycle=4.91556e-08

The 45-th FMG cycle:
 
The maximum norm of residuals after 45 times FMG cycle=4.45429e-07

The 45-th residual reduction rate is about 0.496886

The maximum norm of error after 45 times FMG cycle=2.09359e-08

The 46-th FMG cycle:
 
The maximum norm of residuals after 46 times FMG cycle=2.21922e-07

The 46-th residual reduction rate is about 0.501779

The maximum norm of error after 46 times FMG cycle=7.92939e-09

Obviously, the maximum norm of error has the first order convergence.

\subsection*{III-q n=513,RO=0,IO=0,cycletype=0}

The maximum norm of residuals and errors is shown below.

The 1-th V cycle:

The maximum norm of residuals after 1 times V cycle=19174.9

The 1-th residual reduction rate is about 0.984234

The maximum norm of error after 1 times V cycle=2.28672

The 2-th V cycle:

The maximum norm of residuals after 2 times V cycle=331.602

The 2-th residual reduction rate is about 0.982706

The maximum norm of error after 2 times V cycle=0.129937

The 3-th V cycle:

The maximum norm of residuals after 3 times V cycle=7.14003

The 3-th residual reduction rate is about 0.978468

The maximum norm of error after 3 times V cycle=0.00438296

The 4-th V cycle:

The maximum norm of residuals after 4 times V cycle=0.195432

The 4-th residual reduction rate is about 0.972629

The maximum norm of error after 4 times V cycle=0.000161759

The 5-th V cycle:

The maximum norm of residuals after 5 times V cycle=0.00656199

The 5-th residual reduction rate is about 0.966423

The maximum norm of error after 5 times V cycle=5.87533e-06

The 6-th V cycle:

The maximum norm of residuals after 6 times V cycle=0.000199841

The 6-th residual reduction rate is about 0.969546

The maximum norm of error after 6 times V cycle=2.11294e-07

The 7-th V cycle:

The maximum norm of residuals after 7 times V cycle=6.7724e-06

The 7-th residual reduction rate is about 0.966111

The maximum norm of error after 7 times V cycle=7.396e-09

Obviously, the maximum norm of error has second-order convergence.

\subsection*{III-r n=513,RO=0,IO=0,cycletype=1}

The maximum norm of residuals and errors is shown below.

The 1-th FMG cycle:
 
The maximum norm of residuals after 1 times FMG cycle=33964.1

The 1-th residual reduction rate is about 0.972074

The maximum norm of error after 1 times FMG cycle=2.76139

The 2-th FMG cycle:
 
The maximum norm of residuals after 2 times FMG cycle=5097.96

The 2-th residual reduction rate is about 0.849902

The maximum norm of error after 2 times FMG cycle=0.565019

The 3-th FMG cycle:
 
The maximum norm of residuals after 3 times FMG cycle=1185.37

The 3-th residual reduction rate is about 0.767482

The maximum norm of error after 3 times FMG cycle=0.183122

The 4-th FMG cycle:
 
The maximum norm of residuals after 4 times FMG cycle=361.363

The 4-th residual reduction rate is about 0.695148

The maximum norm of error after 4 times FMG cycle=0.0670893

The 5-th FMG cycle:
 
The maximum norm of residuals after 5 times FMG cycle=113.066

The 5-th residual reduction rate is about 0.687113

The maximum norm of error after 5 times FMG cycle=0.0245978

The 6-th FMG cycle:
 
The maximum norm of residuals after 6 times FMG cycle=36.1165

The 6-th residual reduction rate is about 0.68057

The maximum norm of error after 6 times FMG cycle=0.00901456

The 7-th FMG cycle:
 
The maximum norm of residuals after 7 times FMG cycle=11.7282

The 7-th residual reduction rate is about 0.675267

The maximum norm of error after 7 times FMG cycle=0.00330057

The 8-th FMG cycle:
 
The maximum norm of residuals after 8 times FMG cycle=3.8592

The 8-th residual reduction rate is about 0.670948

The maximum norm of error after 8 times FMG cycle=0.00120623

The 9-th FMG cycle:
 
The maximum norm of residuals after 9 times FMG cycle=1.28355

The 9-th residual reduction rate is about 0.667404

The maximum norm of error after 9 times FMG cycle=0.000440324

The 10-th FMG cycle:
 
The maximum norm of residuals after 10 times FMG cycle=0.430668

The 10-th residual reduction rate is about 0.664472

The maximum norm of error after 10 times FMG cycle=0.000160535

The 11-th FMG cycle:
 
The maximum norm of residuals after 11 times FMG cycle=0.145556

The 11-th residual reduction rate is about 0.662022

The maximum norm of error after 11 times FMG cycle=5.84617e-05

The 12-th FMG cycle:
 
The maximum norm of residuals after 12 times FMG cycle=0.0494958

The 12-th residual reduction rate is about 0.659954

The maximum norm of error after 12 times FMG cycle=2.12777e-05

The 13-th FMG cycle:
 
The maximum norm of residuals after 13 times FMG cycle=0.0169182

The 13-th residual reduction rate is about 0.658189

The maximum norm of error after 13 times FMG cycle=7.73797e-06

The 14-th FMG cycle:
 
The maximum norm of residuals after 14 times FMG cycle=0.00580857

The 14-th residual reduction rate is about 0.656667

The maximum norm of error after 14 times FMG cycle=2.8116e-06

The 15-th FMG cycle:
 
The maximum norm of residuals after 15 times FMG cycle=0.00200199

The 15-th residual reduction rate is about 0.655339

The maximum norm of error after 15 times FMG cycle=1.02062e-06

The 16-th FMG cycle:
 
The maximum norm of residuals after 16 times FMG cycle=0.000692352

The 16-th residual reduction rate is about 0.654168

The maximum norm of error after 16 times FMG cycle=3.70074e-07

The 17-th FMG cycle:
 
The maximum norm of residuals after 17 times FMG cycle=0.000242472

The 17-th residual reduction rate is about 0.649785

The maximum norm of error after 17 times FMG cycle=1.34005e-07

The 18-th FMG cycle:
 
The maximum norm of residuals after 18 times FMG cycle=8.51332e-05

The 18-th residual reduction rate is about 0.648895

The maximum norm of error after 18 times FMG cycle=4.84425e-08

The 19-th FMG cycle:
 
The maximum norm of residuals after 19 times FMG cycle=2.99386e-05

The 19-th residual reduction rate is about 0.648332

The maximum norm of error after 19 times FMG cycle=1.74763e-08

The 20-th FMG cycle:
 
The maximum norm of residuals after 20 times FMG cycle=1.05446e-05

The 20-th residual reduction rate is about 0.647794

The maximum norm of error after 20 times FMG cycle=6.28944e-09

Obviously, the maximum norm of error has the first order convergence.

\subsection*{III-s n=513,RO=0,IO=1,cycletype=0}

The maximum norm of residuals and errors is shown below.

The 1-th V cycle:

The maximum norm of residuals after 1 times V cycle=11393.8

The 1-th residual reduction rate is about 0.990632

The maximum norm of error after 1 times V cycle=2.34175

The 2-th V cycle:

The maximum norm of residuals after 2 times V cycle=258.464

The 2-th residual reduction rate is about 0.977315

The maximum norm of error after 2 times V cycle=0.0269845

The 3-th V cycle:

The maximum norm of residuals after 3 times V cycle=2.75687

The 3-th residual reduction rate is about 0.989334

The maximum norm of error after 3 times V cycle=0.000988651

The 4-th V cycle:

The maximum norm of residuals after 4 times V cycle=0.0676949

The 4-th residual reduction rate is about 0.975445

The maximum norm of error after 4 times V cycle=1.68651e-05

The 5-th V cycle:

The maximum norm of residuals after 5 times V cycle=0.00137793

The 5-th residual reduction rate is about 0.979645

The maximum norm of error after 5 times V cycle=3.99499e-07

The 6-th V cycle:

The maximum norm of residuals after 6 times V cycle=2.90334e-05

The 6-th residual reduction rate is about 0.97893

The maximum norm of error after 6 times V cycle=1.13262e-08

The 7-th V cycle:

The maximum norm of residuals after 7 times V cycle=6.84698e-07

The 7-th residual reduction rate is about 0.976417

The maximum norm of error after 7 times V cycle=1.90894e-10

Obviously, the maximum norm of error has second-order convergence.

\subsection*{III-t n=513,RO=0,IO=1,cycletype=1}

The maximum norm of residuals and errors is shown below.

The 1-th FMG cycle:
 
The maximum norm of residuals after 1 times FMG cycle=50143.9

The 1-th residual reduction rate is about 0.958771

The maximum norm of error after 1 times FMG cycle=3.0309

The 2-th FMG cycle:
 
The maximum norm of residuals after 2 times FMG cycle=11705.6

The 2-th residual reduction rate is about 0.766559

The maximum norm of error after 2 times FMG cycle=0.946954

The 3-th FMG cycle:
 
The maximum norm of residuals after 3 times FMG cycle=3021.69

The 3-th residual reduction rate is about 0.74186

The maximum norm of error after 3 times FMG cycle=0.328545

The 4-th FMG cycle:
 
The maximum norm of residuals after 4 times FMG cycle=920.557

The 4-th residual reduction rate is about 0.69535

The maximum norm of error after 4 times FMG cycle=0.13693

The 5-th FMG cycle:
 
The maximum norm of residuals after 5 times FMG cycle=333.66

The 5-th residual reduction rate is about 0.637545

The maximum norm of error after 5 times FMG cycle=0.0620565

The 6-th FMG cycle:
 
The maximum norm of residuals after 6 times FMG cycle=125.998

The 6-th residual reduction rate is about 0.622376

The maximum norm of error after 6 times FMG cycle=0.0281168

The 7-th FMG cycle:
 
The maximum norm of residuals after 7 times FMG cycle=50.3702

The 7-th residual reduction rate is about 0.600231

The maximum norm of error after 7 times FMG cycle=0.0127291

The 8-th FMG cycle:
 
The maximum norm of residuals after 8 times FMG cycle=20.466

The 8-th residual reduction rate is about 0.593689

The maximum norm of error after 8 times FMG cycle=0.00575298

The 9-th FMG cycle:
 
The maximum norm of residuals after 9 times FMG cycle=8.42665

The 9-th residual reduction rate is about 0.58826

The maximum norm of error after 9 times FMG cycle=0.00259551

The 10-th FMG cycle:
 
The maximum norm of residuals after 10 times FMG cycle=3.50755

The 10-th residual reduction rate is about 0.583755

The maximum norm of error after 10 times FMG cycle=0.00116842

The 11-th FMG cycle:
 
The maximum norm of residuals after 11 times FMG cycle=1.47319

The 11-th residual reduction rate is about 0.579993

The maximum norm of error after 11 times FMG cycle=0.000524842

The 12-th FMG cycle:
 
The maximum norm of residuals after 12 times FMG cycle=0.623429

The 12-th residual reduction rate is about 0.576818

The maximum norm of error after 12 times FMG cycle=0.000235254

The 13-th FMG cycle:
 
The maximum norm of residuals after 13 times FMG cycle=0.265516

The 13-th residual reduction rate is about 0.574105

The maximum norm of error after 13 times FMG cycle=0.00010524

The 14-th FMG cycle:
 
The maximum norm of residuals after 14 times FMG cycle=0.113705

The 14-th residual reduction rate is about 0.571756

The maximum norm of error after 14 times FMG cycle=4.69938e-05

The 15-th FMG cycle:
 
The maximum norm of residuals after 15 times FMG cycle=0.0489276

The 15-th residual reduction rate is about 0.569699

The maximum norm of error after 15 times FMG cycle=2.0951e-05

The 16-th FMG cycle:
 
The maximum norm of residuals after 16 times FMG cycle=0.0211426

The 16-th residual reduction rate is about 0.567879

The maximum norm of error after 16 times FMG cycle=9.32795e-06

The 17-th FMG cycle:
 
The maximum norm of residuals after 17 times FMG cycle=0.00917044

The 17-th residual reduction rate is about 0.566258

The maximum norm of error after 17 times FMG cycle=4.14869e-06

The 18-th FMG cycle:
 
The maximum norm of residuals after 18 times FMG cycle=0.00399093

The 18-th residual reduction rate is about 0.564805

The maximum norm of error after 18 times FMG cycle=1.84383e-06

The 19-th FMG cycle:
 
The maximum norm of residuals after 19 times FMG cycle=0.00174204

The 19-th residual reduction rate is about 0.563501

The maximum norm of error after 19 times FMG cycle=8.19365e-07

The 20-th FMG cycle:
 
The maximum norm of residuals after 20 times FMG cycle=0.000762438

The 20-th residual reduction rate is about 0.562329

The maximum norm of error after 20 times FMG cycle=3.64174e-07

The 21-th FMG cycle:
 
The maximum norm of residuals after 21 times FMG cycle=0.000334498

The 21-th residual reduction rate is about 0.561279

The maximum norm of error after 21 times FMG cycle=1.61924e-07

The 22-th FMG cycle:
 
The maximum norm of residuals after 22 times FMG cycle=0.000147065

The 22-th residual reduction rate is about 0.56034

The maximum norm of error after 22 times FMG cycle=7.20541e-08

The 23-th FMG cycle:
 
The maximum norm of residuals after 23 times FMG cycle=6.47813e-05

The 23-th residual reduction rate is about 0.559506

The maximum norm of error after 23 times FMG cycle=3.28889e-08

The 24-th FMG cycle:
 
The maximum norm of residuals after 24 times FMG cycle=2.85833e-05

The 24-th residual reduction rate is about 0.558772

The maximum norm of error after 24 times FMG cycle=1.61824e-08

The 25-th FMG cycle:
 
The maximum norm of residuals after 25 times FMG cycle=1.26303e-05

The 25-th residual reduction rate is about 0.558125

The maximum norm of error after 25 times FMG cycle=7.89866e-09

Obviously, the maximum norm of error has the first order convergence.

\subsection*{III-u n=513,RO=1,IO=0,cycletype=0}

The maximum norm of residuals and errors is shown below.

The 1-th V cycle:

The maximum norm of residuals after 1 times V cycle=39011.3

The 1-th residual reduction rate is about 0.967924

The maximum norm of error after 1 times V cycle=1.9608

The 2-th V cycle:

The maximum norm of residuals after 2 times V cycle=2677.3

The 2-th residual reduction rate is about 0.931371

The maximum norm of error after 2 times V cycle=2.05373

The 3-th V cycle:

The maximum norm of residuals after 3 times V cycle=209.184

The 3-th residual reduction rate is about 0.921868

The maximum norm of error after 3 times V cycle=0.0952628

The 4-th V cycle:

The maximum norm of residuals after 4 times V cycle=21.1261

The 4-th residual reduction rate is about 0.899007

The maximum norm of error after 4 times V cycle=0.050419

The 5-th V cycle:

The maximum norm of residuals after 5 times V cycle=1.79633

The 5-th residual reduction rate is about 0.914971

The maximum norm of error after 5 times V cycle=0.0033314

The 6-th V cycle:

The maximum norm of residuals after 6 times V cycle=0.188614

The 6-th residual reduction rate is about 0.895

The maximum norm of error after 6 times V cycle=0.000887299

The 7-th V cycle:

The maximum norm of residuals after 7 times V cycle=0.0191387

The 7-th residual reduction rate is about 0.89853

The maximum norm of error after 7 times V cycle=7.37768e-05

The 8-th V cycle:

The maximum norm of residuals after 8 times V cycle=0.00207604

The 8-th residual reduction rate is about 0.891526

The maximum norm of error after 8 times V cycle=1.41856e-05

The 9-th V cycle:

The maximum norm of residuals after 9 times V cycle=0.000183009

The 9-th residual reduction rate is about 0.911847

The maximum norm of error after 9 times V cycle=1.49296e-06

The 10-th V cycle:

The maximum norm of residuals after 10 times V cycle=2.26588e-05

The 10-th residual reduction rate is about 0.876188

The maximum norm of error after 10 times V cycle=2.20614e-07

The 11-th V cycle:

The maximum norm of residuals after 11 times V cycle=2.13919e-06

The 11-th residual reduction rate is about 0.905591

The maximum norm of error after 11 times V cycle=2.38675e-08

The 12-th V cycle:

The maximum norm of residuals after 12 times V cycle=2.5275e-07

The 12-th residual reduction rate is about 0.881848

The maximum norm of error after 12 times V cycle=3.35787e-09

Obviously, the maximum norm of error has second-order convergence.

\subsection*{III-v n=513,RO=1,IO=0,cycletype=1}

The maximum norm of residuals and errors is shown below.

The 1-th FMG cycle:
 
The maximum norm of residuals after 1 times FMG cycle=57010.4

The 1-th residual reduction rate is about 0.953125

The maximum norm of error after 1 times FMG cycle=1.68559

The 2-th FMG cycle:
 
The maximum norm of residuals after 2 times FMG cycle=20030.9

The 2-th residual reduction rate is about 0.648645

The maximum norm of error after 2 times FMG cycle=2.41453

The 3-th FMG cycle:
 
The maximum norm of residuals after 3 times FMG cycle=10948

The 3-th residual reduction rate is about 0.453443

The maximum norm of error after 3 times FMG cycle=2.94265

The 4-th FMG cycle:
 
The maximum norm of residuals after 4 times FMG cycle=7372.91

The 4-th residual reduction rate is about 0.326553

The maximum norm of error after 4 times FMG cycle=4.41058

The 5-th FMG cycle:
 
The maximum norm of residuals after 5 times FMG cycle=4508.77

The 5-th residual reduction rate is about 0.388468

The maximum norm of error after 5 times FMG cycle=4.74552

The 6-th FMG cycle:
 
The maximum norm of residuals after 6 times FMG cycle=3938.06

The 6-th residual reduction rate is about 0.126577

The maximum norm of error after 6 times FMG cycle=4.84297

The 7-th FMG cycle:
 
The maximum norm of residuals after 7 times FMG cycle=3025.62

The 7-th residual reduction rate is about 0.231697

The maximum norm of error after 7 times FMG cycle=4.82998

The 8-th FMG cycle:
 
The maximum norm of residuals after 8 times FMG cycle=2130.55

The 8-th residual reduction rate is about 0.29583

The maximum norm of error after 8 times FMG cycle=4.46951

The 9-th FMG cycle:
 
The maximum norm of residuals after 9 times FMG cycle=1410.24

The 9-th residual reduction rate is about 0.338087

The maximum norm of error after 9 times FMG cycle=4.3038

The 10-th FMG cycle:
 
The maximum norm of residuals after 10 times FMG cycle=917.625

The 10-th residual reduction rate is about 0.349314

The maximum norm of error after 10 times FMG cycle=4.68975

The 11-th FMG cycle:
 
The maximum norm of residuals after 11 times FMG cycle=678.648

The 11-th residual reduction rate is about 0.260429

The maximum norm of error after 11 times FMG cycle=6.71447

The 12-th FMG cycle:
 
The maximum norm of residuals after 12 times FMG cycle=568.027

The 12-th residual reduction rate is about 0.163002

The maximum norm of error after 12 times FMG cycle=7.48032

The 13-th FMG cycle:
 
The maximum norm of residuals after 13 times FMG cycle=529.9

The 13-th residual reduction rate is about 0.0671225

The maximum norm of error after 13 times FMG cycle=7.04625

The 14-th FMG cycle:
 
The maximum norm of residuals after 14 times FMG cycle=450.489

The 14-th residual reduction rate is about 0.14986

The maximum norm of error after 14 times FMG cycle=5.75904

The 15-th FMG cycle:
 
The maximum norm of residuals after 15 times FMG cycle=356.568

The 15-th residual reduction rate is about 0.208488

The maximum norm of error after 15 times FMG cycle=4.05474

The 16-th FMG cycle:
 
The maximum norm of residuals after 16 times FMG cycle=266.333

The 16-th residual reduction rate is about 0.253065

The maximum norm of error after 16 times FMG cycle=2.32447

The 17-th FMG cycle:
 
The maximum norm of residuals after 17 times FMG cycle=202.006

The 17-th residual reduction rate is about 0.241527

The maximum norm of error after 17 times FMG cycle=1.10714

The 18-th FMG cycle:
 
The maximum norm of residuals after 18 times FMG cycle=155.256

The 18-th residual reduction rate is about 0.231429

The maximum norm of error after 18 times FMG cycle=1.19321

The 19-th FMG cycle:
 
The maximum norm of residuals after 19 times FMG cycle=113.373

The 19-th residual reduction rate is about 0.269769

The maximum norm of error after 19 times FMG cycle=1.5903

The 20-th FMG cycle:
 
The maximum norm of residuals after 20 times FMG cycle=78.7646

The 20-th residual reduction rate is about 0.305261

The maximum norm of error after 20 times FMG cycle=1.74531

The 21-th FMG cycle:
 
The maximum norm of residuals after 21 times FMG cycle=59.8784

The 21-th residual reduction rate is about 0.23978

The maximum norm of error after 21 times FMG cycle=1.7142

The 22-th FMG cycle:
 
The maximum norm of residuals after 22 times FMG cycle=46.1726

The 22-th residual reduction rate is about 0.228894

The maximum norm of error after 22 times FMG cycle=1.56547

The 23-th FMG cycle:
 
The maximum norm of residuals after 23 times FMG cycle=34.5339

The 23-th residual reduction rate is about 0.25207

The maximum norm of error after 23 times FMG cycle=1.36117

The 24-th FMG cycle:
 
The maximum norm of residuals after 24 times FMG cycle=25.1026

The 24-th residual reduction rate is about 0.273103

The maximum norm of error after 24 times FMG cycle=1.16233

The 25-th FMG cycle:
 
The maximum norm of residuals after 25 times FMG cycle=21.3026

The 25-th residual reduction rate is about 0.151379

The maximum norm of error after 25 times FMG cycle=1.0021

The 26-th FMG cycle:
 
The maximum norm of residuals after 26 times FMG cycle=18.2877

The 26-th residual reduction rate is about 0.141525

The maximum norm of error after 26 times FMG cycle=0.858978

The 27-th FMG cycle:
 
The maximum norm of residuals after 27 times FMG cycle=15.3398

The 27-th residual reduction rate is about 0.161194

The maximum norm of error after 27 times FMG cycle=0.734419

The 28-th FMG cycle:
 
The maximum norm of residuals after 28 times FMG cycle=12.5745

The 28-th residual reduction rate is about 0.18027

The maximum norm of error after 28 times FMG cycle=0.625295

The 29-th FMG cycle:
 
The maximum norm of residuals after 29 times FMG cycle=10.0653

The 29-th residual reduction rate is about 0.19955

The maximum norm of error after 29 times FMG cycle=0.527809

The 30-th FMG cycle:
 
The maximum norm of residuals after 30 times FMG cycle=7.85571

The 30-th residual reduction rate is about 0.219524

The maximum norm of error after 30 times FMG cycle=0.439331

The 31-th FMG cycle:
 
The maximum norm of residuals after 31 times FMG cycle=5.96597

The 31-th residual reduction rate is about 0.240556

The maximum norm of error after 31 times FMG cycle=0.358787

The 32-th FMG cycle:
 
The maximum norm of residuals after 32 times FMG cycle=4.39678

The 32-th residual reduction rate is about 0.263023

The maximum norm of error after 32 times FMG cycle=0.28632

The 33-th FMG cycle:
 
The maximum norm of residuals after 33 times FMG cycle=3.39445

The 33-th residual reduction rate is about 0.22797

The maximum norm of error after 33 times FMG cycle=0.222572

The 34-th FMG cycle:
 
The maximum norm of residuals after 34 times FMG cycle=2.57415

The 34-th residual reduction rate is about 0.24166

The maximum norm of error after 34 times FMG cycle=0.168144

The 35-th FMG cycle:
 
The maximum norm of residuals after 35 times FMG cycle=1.90209

The 35-th residual reduction rate is about 0.261078

The maximum norm of error after 35 times FMG cycle=0.123231

The 36-th FMG cycle:
 
The maximum norm of residuals after 36 times FMG cycle=1.36856

The 36-th residual reduction rate is about 0.280498

The maximum norm of error after 36 times FMG cycle=0.0874978

The 37-th FMG cycle:
 
The maximum norm of residuals after 37 times FMG cycle=0.957767

The 37-th residual reduction rate is about 0.300164

The maximum norm of error after 37 times FMG cycle=0.0601274

The 38-th FMG cycle:
 
The maximum norm of residuals after 38 times FMG cycle=0.650856

The 38-th residual reduction rate is about 0.320444

The maximum norm of error after 38 times FMG cycle=0.0399721

The 39-th FMG cycle:
 
The maximum norm of residuals after 39 times FMG cycle=0.434442

The 39-th residual reduction rate is about 0.332507

The maximum norm of error after 39 times FMG cycle=0.0257247

The 40-th FMG cycle:
 
The maximum norm of residuals after 40 times FMG cycle=0.355607

The 40-th residual reduction rate is about 0.181463

The maximum norm of error after 40 times FMG cycle=0.0160795

The 41-th FMG cycle:
 
The maximum norm of residuals after 41 times FMG cycle=0.282496

The 41-th residual reduction rate is about 0.205595

The maximum norm of error after 41 times FMG cycle=0.00984474

The 42-th FMG cycle:
 
The maximum norm of residuals after 42 times FMG cycle=0.217644

The 42-th residual reduction rate is about 0.229566

The maximum norm of error after 42 times FMG cycle=0.0064713

The 43-th FMG cycle:
 
The maximum norm of residuals after 43 times FMG cycle=0.162447

The 43-th residual reduction rate is about 0.253614

The maximum norm of error after 43 times FMG cycle=0.00474754

The 44-th FMG cycle:
 
The maximum norm of residuals after 44 times FMG cycle=0.119511

The 44-th residual reduction rate is about 0.264307

The maximum norm of error after 44 times FMG cycle=0.00357933

The 45-th FMG cycle:
 
The maximum norm of residuals after 45 times FMG cycle=0.0900313

The 45-th residual reduction rate is about 0.24667

The maximum norm of error after 45 times FMG cycle=0.00272846

The 46-th FMG cycle:
 
The maximum norm of residuals after 46 times FMG cycle=0.0702262

The 46-th residual reduction rate is about 0.21998

The maximum norm of error after 46 times FMG cycle=0.00207395

The 47-th FMG cycle:
 
The maximum norm of residuals after 47 times FMG cycle=0.0535782

The 47-th residual reduction rate is about 0.237062

The maximum norm of error after 47 times FMG cycle=0.00155014

The 48-th FMG cycle:
 
The maximum norm of residuals after 48 times FMG cycle=0.0398947

The 48-th residual reduction rate is about 0.255394

The maximum norm of error after 48 times FMG cycle=0.00112089

The 49-th FMG cycle:
 
The maximum norm of residuals after 49 times FMG cycle=0.0292939

The 49-th residual reduction rate is about 0.26572

The maximum norm of error after 49 times FMG cycle=0.000765906

The 50-th FMG cycle:
 
The maximum norm of residuals after 50 times FMG cycle=0.020859

The 50-th residual reduction rate is about 0.287938

The maximum norm of error after 50 times FMG cycle=0.000475725

The 51-th FMG cycle:
 
The maximum norm of residuals after 51 times FMG cycle=0.01537

The 51-th residual reduction rate is about 0.263147

The maximum norm of error after 51 times FMG cycle=0.000245483

The 52-th FMG cycle:
 
The maximum norm of residuals after 52 times FMG cycle=0.0127848

The 52-th residual reduction rate is about 0.168203

The maximum norm of error after 52 times FMG cycle=9.5807e-05

The 53-th FMG cycle:
 
The maximum norm of residuals after 53 times FMG cycle=0.0102646

The 53-th residual reduction rate is about 0.197119

The maximum norm of error after 53 times FMG cycle=0.00014576

The 54-th FMG cycle:
 
The maximum norm of residuals after 54 times FMG cycle=0.00875379

The 54-th residual reduction rate is about 0.14719

The maximum norm of error after 54 times FMG cycle=0.000190179

The 55-th FMG cycle:
 
The maximum norm of residuals after 55 times FMG cycle=0.00779863

The 55-th residual reduction rate is about 0.109113

The maximum norm of error after 55 times FMG cycle=0.000214935

The 56-th FMG cycle:
 
The maximum norm of residuals after 56 times FMG cycle=0.00660364

The 56-th residual reduction rate is about 0.153232

The maximum norm of error after 56 times FMG cycle=0.000222271

The 57-th FMG cycle:
 
The maximum norm of residuals after 57 times FMG cycle=0.00535803

The 57-th residual reduction rate is about 0.188624

The maximum norm of error after 57 times FMG cycle=0.000214038

The 58-th FMG cycle:
 
The maximum norm of residuals after 58 times FMG cycle=0.00423253

The 58-th residual reduction rate is about 0.210058

The maximum norm of error after 58 times FMG cycle=0.000194963

The 59-th FMG cycle:
 
The maximum norm of residuals after 59 times FMG cycle=0.00323914

The 59-th residual reduction rate is about 0.234704

The maximum norm of error after 59 times FMG cycle=0.000169648

The 60-th FMG cycle:
 
The maximum norm of residuals after 60 times FMG cycle=0.00238435

The 60-th residual reduction rate is about 0.263894

The maximum norm of error after 60 times FMG cycle=0.000141679

The 61-th FMG cycle:
 
The maximum norm of residuals after 61 times FMG cycle=0.00168227

The 61-th residual reduction rate is about 0.294454

The maximum norm of error after 61 times FMG cycle=0.000113811

The 62-th FMG cycle:
 
The maximum norm of residuals after 62 times FMG cycle=0.00124246

The 62-th residual reduction rate is about 0.261435

The maximum norm of error after 62 times FMG cycle=8.79724e-05

The 63-th FMG cycle:
 
The maximum norm of residuals after 63 times FMG cycle=0.000912502

The 63-th residual reduction rate is about 0.265572

The maximum norm of error after 63 times FMG cycle=6.53184e-05

The 64-th FMG cycle:
 
The maximum norm of residuals after 64 times FMG cycle=0.000732122

The 64-th residual reduction rate is about 0.197676

The maximum norm of error after 64 times FMG cycle=4.63676e-05

The 65-th FMG cycle:
 
The maximum norm of residuals after 65 times FMG cycle=0.000570018

The 65-th residual reduction rate is about 0.221417

The maximum norm of error after 65 times FMG cycle=3.11747e-05

The 66-th FMG cycle:
 
The maximum norm of residuals after 66 times FMG cycle=0.000431437

The 66-th residual reduction rate is about 0.243117

The maximum norm of error after 66 times FMG cycle=1.94857e-05

The 67-th FMG cycle:
 
The maximum norm of residuals after 67 times FMG cycle=0.000353786

The 67-th residual reduction rate is about 0.179981

The maximum norm of error after 67 times FMG cycle=1.08691e-05

The 68-th FMG cycle:
 
The maximum norm of residuals after 68 times FMG cycle=0.000295659

The 68-th residual reduction rate is about 0.164301

The maximum norm of error after 68 times FMG cycle=4.813e-06

The 69-th FMG cycle:
 
The maximum norm of residuals after 69 times FMG cycle=0.000238209

The 69-th residual reduction rate is about 0.194313

The maximum norm of error after 69 times FMG cycle=1.91057e-06

The 70-th FMG cycle:
 
The maximum norm of residuals after 70 times FMG cycle=0.000185599

The 70-th residual reduction rate is about 0.220855

The maximum norm of error after 70 times FMG cycle=2.7433e-06

The 71-th FMG cycle:
 
The maximum norm of residuals after 71 times FMG cycle=0.00013998

The 71-th residual reduction rate is about 0.245792

The maximum norm of error after 71 times FMG cycle=3.35073e-06

The 72-th FMG cycle:
 
The maximum norm of residuals after 72 times FMG cycle=0.000102101

The 72-th residual reduction rate is about 0.270601

The maximum norm of error after 72 times FMG cycle=3.61093e-06

The 73-th FMG cycle:
 
The maximum norm of residuals after 73 times FMG cycle=7.18028e-05

The 73-th residual reduction rate is about 0.29675

The maximum norm of error after 73 times FMG cycle=3.58143e-06

The 74-th FMG cycle:
 
The maximum norm of residuals after 74 times FMG cycle=5.5212e-05

The 74-th residual reduction rate is about 0.231061

The maximum norm of error after 74 times FMG cycle=3.28954e-06

The 75-th FMG cycle:
 
The maximum norm of residuals after 75 times FMG cycle=4.23206e-05

The 75-th residual reduction rate is about 0.23349

The maximum norm of error after 75 times FMG cycle=2.84204e-06

The 76-th FMG cycle:
 
The maximum norm of residuals after 76 times FMG cycle=3.47315e-05

The 76-th residual reduction rate is about 0.179324

The maximum norm of error after 76 times FMG cycle=2.34091e-06

The 77-th FMG cycle:
 
The maximum norm of residuals after 77 times FMG cycle=2.78228e-05

The 77-th residual reduction rate is about 0.198916

The maximum norm of error after 77 times FMG cycle=1.85133e-06

The 78-th FMG cycle:
 
The maximum norm of residuals after 78 times FMG cycle=2.16693e-05

The 78-th residual reduction rate is about 0.221167

The maximum norm of error after 78 times FMG cycle=1.41094e-06

The 79-th FMG cycle:
 
The maximum norm of residuals after 79 times FMG cycle=1.64451e-05

The 79-th residual reduction rate is about 0.241089

The maximum norm of error after 79 times FMG cycle=1.03705e-06

The 80-th FMG cycle:
 
The maximum norm of residuals after 80 times FMG cycle=1.21761e-05

The 80-th residual reduction rate is about 0.259589

The maximum norm of error after 80 times FMG cycle=7.34173e-07

The 81-th FMG cycle:
 
The maximum norm of residuals after 81 times FMG cycle=8.79879e-06

The 81-th residual reduction rate is about 0.277372

The maximum norm of error after 81 times FMG cycle=4.9882e-07

The 82-th FMG cycle:
 
The maximum norm of residuals after 82 times FMG cycle=6.27978e-06

The 82-th residual reduction rate is about 0.286291

The maximum norm of error after 82 times FMG cycle=3.23029e-07

The 83-th FMG cycle:
 
The maximum norm of residuals after 83 times FMG cycle=4.50633e-06

The 83-th residual reduction rate is about 0.282406

The maximum norm of error after 83 times FMG cycle=1.96858e-07

The 84-th FMG cycle:
 
The maximum norm of residuals after 84 times FMG cycle=3.15939e-06

The 84-th residual reduction rate is about 0.298901

The maximum norm of error after 84 times FMG cycle=1.10095e-07

The 85-th FMG cycle:
 
The maximum norm of residuals after 85 times FMG cycle=2.41101e-06

The 85-th residual reduction rate is about 0.236873

The maximum norm of error after 85 times FMG cycle=5.33165e-08

The 86-th FMG cycle:
 
The maximum norm of residuals after 86 times FMG cycle=1.96201e-06

The 86-th residual reduction rate is about 0.186229

The maximum norm of error after 86 times FMG cycle=1.83995e-08

The 87-th FMG cycle:
 
The maximum norm of residuals after 87 times FMG cycle=1.54302e-06

The 87-th residual reduction rate is about 0.213553

The maximum norm of error after 87 times FMG cycle=1.44007e-08

The 88-th FMG cycle:
 
The maximum norm of residuals after 88 times FMG cycle=1.17772e-06

The 88-th residual reduction rate is about 0.236741

The maximum norm of error after 88 times FMG cycle=1.70045e-08

The 89-th FMG cycle:
 
The maximum norm of residuals after 89 times FMG cycle=8.74214e-07

The 89-th residual reduction rate is about 0.257709

The maximum norm of error after 89 times FMG cycle=1.6598e-08

The 90-th FMG cycle:
 
The maximum norm of residuals after 90 times FMG cycle=6.51605e-07

The 90-th residual reduction rate is about 0.254639

The maximum norm of error after 90 times FMG cycle=1.48343e-08

The 91-th FMG cycle:
 
The maximum norm of residuals after 91 times FMG cycle=4.75412e-07

The 91-th residual reduction rate is about 0.270399

The maximum norm of error after 91 times FMG cycle=1.26598e-08

The 92-th FMG cycle:
 
The maximum norm of residuals after 92 times FMG cycle=3.39612e-07

The 92-th residual reduction rate is about 0.285646

The maximum norm of error after 92 times FMG cycle=9.91397e-09

Obviously, the maximum norm of error has the first order convergence.

\subsection*{III-w n=513,RO=1,IO=1,cycletype=0}

The maximum norm of residuals and errors is shown below.

The 1-th V cycle:

The maximum norm of residuals after 1 times V cycle=28929.8

The 1-th residual reduction rate is about 0.976214

The maximum norm of error after 1 times V cycle=1.99587

The 2-th V cycle:

The maximum norm of residuals after 2 times V cycle=1496.71

The 2-th residual reduction rate is about 0.948264

The maximum norm of error after 2 times V cycle=2.20384

The 3-th V cycle:

The maximum norm of residuals after 3 times V cycle=95.2229

The 3-th residual reduction rate is about 0.936378

The maximum norm of error after 3 times V cycle=0.203811

The 4-th V cycle:

The maximum norm of residuals after 4 times V cycle=4.48456

The 4-th residual reduction rate is about 0.952905

The maximum norm of error after 4 times V cycle=0.00645516

The 5-th V cycle:

The maximum norm of residuals after 5 times V cycle=0.356607

The 5-th residual reduction rate is about 0.920481

The maximum norm of error after 5 times V cycle=0.000280104

The 6-th V cycle:

The maximum norm of residuals after 6 times V cycle=0.0158615

The 6-th residual reduction rate is about 0.955521

The maximum norm of error after 6 times V cycle=4.70519e-05

The 7-th V cycle:

The maximum norm of residuals after 7 times V cycle=0.000933876

The 7-th residual reduction rate is about 0.941123

The maximum norm of error after 7 times V cycle=2.39142e-06

The 8-th V cycle:

The maximum norm of residuals after 8 times V cycle=8.3329e-05

The 8-th residual reduction rate is about 0.910771

The maximum norm of error after 8 times V cycle=6.2497e-08

The 9-th V cycle:

The maximum norm of residuals after 9 times V cycle=4.40666e-06

The 9-th residual reduction rate is about 0.947117

The maximum norm of error after 9 times V cycle=4.72664e-09

Obviously, the maximum norm of error has second-order convergence.

\subsection*{III-x n=513,RO=1,IO=1,cycletype=1}

The maximum norm of residuals and errors is shown below.

The 1-th FMG cycle:
 
The maximum norm of residuals after 1 times FMG cycle=57010.4

The 1-th residual reduction rate is about 0.953125

The maximum norm of error after 1 times FMG cycle=1.6856

The 2-th FMG cycle:
 
The maximum norm of residuals after 2 times FMG cycle=21653

The 2-th residual reduction rate is about 0.620192

The maximum norm of error after 2 times FMG cycle=2.58555

The 3-th FMG cycle:
 
The maximum norm of residuals after 3 times FMG cycle=9883.18

The 3-th residual reduction rate is about 0.543565

The maximum norm of error after 3 times FMG cycle=2.89961

The 4-th FMG cycle:
 
The maximum norm of residuals after 4 times FMG cycle=5110.12

The 4-th residual reduction rate is about 0.482948

The maximum norm of error after 4 times FMG cycle=3.93249

The 5-th FMG cycle:
 
The maximum norm of residuals after 5 times FMG cycle=2386.27

The 5-th residual reduction rate is about 0.53303

The maximum norm of error after 5 times FMG cycle=3.63763

The 6-th FMG cycle:
 
The maximum norm of residuals after 6 times FMG cycle=1186.02

The 6-th residual reduction rate is about 0.502981

The maximum norm of error after 6 times FMG cycle=3.82182

The 7-th FMG cycle:
 
The maximum norm of residuals after 7 times FMG cycle=671.116

The 7-th residual reduction rate is about 0.434146

The maximum norm of error after 7 times FMG cycle=4.13597

The 8-th FMG cycle:
 
The maximum norm of residuals after 8 times FMG cycle=366.113

The 8-th residual reduction rate is about 0.454472

The maximum norm of error after 8 times FMG cycle=4.16318

The 9-th FMG cycle:
 
The maximum norm of residuals after 9 times FMG cycle=246.986

The 9-th residual reduction rate is about 0.325382

The maximum norm of error after 9 times FMG cycle=4.09546

The 10-th FMG cycle:
 
The maximum norm of residuals after 10 times FMG cycle=168.827

The 10-th residual reduction rate is about 0.316453

The maximum norm of error after 10 times FMG cycle=3.59528

The 11-th FMG cycle:
 
The maximum norm of residuals after 11 times FMG cycle=103.739

The 11-th residual reduction rate is about 0.385528

The maximum norm of error after 11 times FMG cycle=2.88121

The 12-th FMG cycle:
 
The maximum norm of residuals after 12 times FMG cycle=58.3941

The 12-th residual reduction rate is about 0.437106

The maximum norm of error after 12 times FMG cycle=2.16708

The 13-th FMG cycle:
 
The maximum norm of residuals after 13 times FMG cycle=33.5868

The 13-th residual reduction rate is about 0.424825

The maximum norm of error after 13 times FMG cycle=1.55957

The 14-th FMG cycle:
 
The maximum norm of residuals after 14 times FMG cycle=19.026

The 14-th residual reduction rate is about 0.433528

The maximum norm of error after 14 times FMG cycle=1.0859

The 15-th FMG cycle:
 
The maximum norm of residuals after 15 times FMG cycle=11.0707

The 15-th residual reduction rate is about 0.418126

The maximum norm of error after 15 times FMG cycle=0.736065

The 16-th FMG cycle:
 
The maximum norm of residuals after 16 times FMG cycle=6.94487

The 16-th residual reduction rate is about 0.372681

The maximum norm of error after 16 times FMG cycle=0.487769

The 17-th FMG cycle:
 
The maximum norm of residuals after 17 times FMG cycle=4.48159

The 17-th residual reduction rate is about 0.354691

The maximum norm of error after 17 times FMG cycle=0.317417

The 18-th FMG cycle:
 
The maximum norm of residuals after 18 times FMG cycle=2.85696

The 18-th residual reduction rate is about 0.362511

The maximum norm of error after 18 times FMG cycle=0.204075

The 19-th FMG cycle:
 
The maximum norm of residuals after 19 times FMG cycle=1.73295

The 19-th residual reduction rate is about 0.39343

The maximum norm of error after 19 times FMG cycle=0.130728

The 20-th FMG cycle:
 
The maximum norm of residuals after 20 times FMG cycle=1.05106

The 20-th residual reduction rate is about 0.393482

The maximum norm of error after 20 times FMG cycle=0.0872946

The 21-th FMG cycle:
 
The maximum norm of residuals after 21 times FMG cycle=0.779279

The 21-th residual reduction rate is about 0.25858

The maximum norm of error after 21 times FMG cycle=0.0608459

The 22-th FMG cycle:
 
The maximum norm of residuals after 22 times FMG cycle=0.565557

The 22-th residual reduction rate is about 0.274257

The maximum norm of error after 22 times FMG cycle=0.0425842

The 23-th FMG cycle:
 
The maximum norm of residuals after 23 times FMG cycle=0.401131

The 23-th residual reduction rate is about 0.290732

The maximum norm of error after 23 times FMG cycle=0.0296975

The 24-th FMG cycle:
 
The maximum norm of residuals after 24 times FMG cycle=0.278374

The 24-th residual reduction rate is about 0.306027

The maximum norm of error after 24 times FMG cycle=0.0205028

The 25-th FMG cycle:
 
The maximum norm of residuals after 25 times FMG cycle=0.188614

The 25-th residual reduction rate is about 0.322444

The maximum norm of error after 25 times FMG cycle=0.0139436

The 26-th FMG cycle:
 
The maximum norm of residuals after 26 times FMG cycle=0.124691

The 26-th residual reduction rate is about 0.338909

The maximum norm of error after 26 times FMG cycle=0.00930715

The 27-th FMG cycle:
 
The maximum norm of residuals after 27 times FMG cycle=0.0804645

The 27-th residual reduction rate is about 0.354689

The maximum norm of error after 27 times FMG cycle=0.00608045

The 28-th FMG cycle:
 
The maximum norm of residuals after 28 times FMG cycle=0.0513101

The 28-th residual reduction rate is about 0.362326

The maximum norm of error after 28 times FMG cycle=0.00387944

The 29-th FMG cycle:
 
The maximum norm of residuals after 29 times FMG cycle=0.0325544

The 29-th residual reduction rate is about 0.365537

The maximum norm of error after 29 times FMG cycle=0.00241224

The 30-th FMG cycle:
 
The maximum norm of residuals after 30 times FMG cycle=0.0202752

The 30-th residual reduction rate is about 0.377191

The maximum norm of error after 30 times FMG cycle=0.00145851

The 31-th FMG cycle:
 
The maximum norm of residuals after 31 times FMG cycle=0.0124139

The 31-th residual reduction rate is about 0.38773

The maximum norm of error after 31 times FMG cycle=0.000855052

The 32-th FMG cycle:
 
The maximum norm of residuals after 32 times FMG cycle=0.00745673

The 32-th residual reduction rate is about 0.399323

The maximum norm of error after 32 times FMG cycle=0.000484079

The 33-th FMG cycle:
 
The maximum norm of residuals after 33 times FMG cycle=0.00438097

The 33-th residual reduction rate is about 0.412481

The maximum norm of error after 33 times FMG cycle=0.000263045

The 34-th FMG cycle:
 
The maximum norm of residuals after 34 times FMG cycle=0.00251346

The 34-th residual reduction rate is about 0.426277

The maximum norm of error after 34 times FMG cycle=0.000135825

The 35-th FMG cycle:
 
The maximum norm of residuals after 35 times FMG cycle=0.00140554

The 35-th residual reduction rate is about 0.440796

The maximum norm of error after 35 times FMG cycle=6.54746e-05

The 36-th FMG cycle:
 
The maximum norm of residuals after 36 times FMG cycle=0.000797665

The 36-th residual reduction rate is about 0.432485

The maximum norm of error after 36 times FMG cycle=2.85314e-05

The 37-th FMG cycle:
 
The maximum norm of residuals after 37 times FMG cycle=0.000451238

The 37-th residual reduction rate is about 0.434302

The maximum norm of error after 37 times FMG cycle=1.34679e-05

The 38-th FMG cycle:
 
The maximum norm of residuals after 38 times FMG cycle=0.000251564

The 38-th residual reduction rate is about 0.442502

The maximum norm of error after 38 times FMG cycle=1.20398e-05

The 39-th FMG cycle:
 
The maximum norm of residuals after 39 times FMG cycle=0.000137328

The 39-th residual reduction rate is about 0.454104

The maximum norm of error after 39 times FMG cycle=9.86393e-06

The 40-th FMG cycle:
 
The maximum norm of residuals after 40 times FMG cycle=7.27105e-05

The 40-th residual reduction rate is about 0.470534

The maximum norm of error after 40 times FMG cycle=7.60021e-06

The 41-th FMG cycle:
 
The maximum norm of residuals after 41 times FMG cycle=4.59014e-05

The 41-th residual reduction rate is about 0.36871

The maximum norm of error after 41 times FMG cycle=5.59459e-06

The 42-th FMG cycle:
 
The maximum norm of residuals after 42 times FMG cycle=2.98343e-05

The 42-th residual reduction rate is about 0.350036

The maximum norm of error after 42 times FMG cycle=3.97674e-06

The 43-th FMG cycle:
 
The maximum norm of residuals after 43 times FMG cycle=1.92325e-05

The 43-th residual reduction rate is about 0.355356

The maximum norm of error after 43 times FMG cycle=2.75095e-06

The 44-th FMG cycle:
 
The maximum norm of residuals after 44 times FMG cycle=1.22918e-05

The 44-th residual reduction rate is about 0.360885

The maximum norm of error after 44 times FMG cycle=1.86316e-06

The 45-th FMG cycle:
 
The maximum norm of residuals after 45 times FMG cycle=7.79908e-06

The 45-th residual reduction rate is about 0.365503

The maximum norm of error after 45 times FMG cycle=1.24128e-06

The 46-th FMG cycle:
 
The maximum norm of residuals after 46 times FMG cycle=4.91824e-06

The 46-th residual reduction rate is about 0.369382

The maximum norm of error after 46 times FMG cycle=8.16494e-07

The 47-th FMG cycle:
 
The maximum norm of residuals after 47 times FMG cycle=3.08554e-06

The 47-th residual reduction rate is about 0.372633

The maximum norm of error after 47 times FMG cycle=5.31794e-07

The 48-th FMG cycle:
 
The maximum norm of residuals after 48 times FMG cycle=2.08174e-06

The 48-th residual reduction rate is about 0.325326

The maximum norm of error after 48 times FMG cycle=3.43721e-07

The 49-th FMG cycle:
 
The maximum norm of residuals after 49 times FMG cycle=1.39408e-06

The 49-th residual reduction rate is about 0.330331

The maximum norm of error after 49 times FMG cycle=2.20813e-07

The 50-th FMG cycle:
 
The maximum norm of residuals after 50 times FMG cycle=9.2259e-07

The 50-th residual reduction rate is about 0.338207

The maximum norm of error after 50 times FMG cycle=1.41152e-07

The 51-th FMG cycle:
 
The maximum norm of residuals after 51 times FMG cycle=6.0443e-07

The 51-th residual reduction rate is about 0.344855

The maximum norm of error after 51 times FMG cycle=8.98409e-08

The 52-th FMG cycle:
 
The maximum norm of residuals after 52 times FMG cycle=3.92667e-07

The 52-th residual reduction rate is about 0.350352

The maximum norm of error after 52 times FMG cycle=5.69428e-08

The 53-th FMG cycle:
 
The maximum norm of residuals after 53 times FMG cycle=2.53089e-07

The 53-th residual reduction rate is about 0.355462

The maximum norm of error after 53 times FMG cycle=3.59443e-08

The 54-th FMG cycle:
 
The maximum norm of residuals after 54 times FMG cycle=1.61816e-07

The 54-th residual reduction rate is about 0.360637

The maximum norm of error after 54 times FMG cycle=2.26137e-08

The 55-th FMG cycle:
 
The maximum norm of residuals after 55 times FMG cycle=1.02797e-07

The 55-th residual reduction rate is about 0.36473

The maximum norm of error after 55 times FMG cycle=1.41873e-08

The 56-th FMG cycle:
 
The maximum norm of residuals after 56 times FMG cycle=6.4958e-08

The 56-th residual reduction rate is about 0.368092

The maximum norm of error after 56 times FMG cycle=8.86498e-09

Obviously, the maximum norm of error has the first order convergence.

\subsection*{III-y n=1025,RO=0,IO=0,cycletype=0}

The maximum norm of residuals and errors is shown below.

The 1-th V cycle:

The maximum norm of residuals after 1 times V cycle=76699.1

The 1-th residual reduction rate is about 0.984234

The maximum norm of error after 1 times V cycle=2.28787

The 2-th V cycle:

The maximum norm of residuals after 2 times V cycle=1326.4

The 2-th residual reduction rate is about 0.982706

The maximum norm of error after 2 times V cycle=0.130303

The 3-th V cycle:

The maximum norm of residuals after 3 times V cycle=28.5602

The 3-th residual reduction rate is about 0.978468

The maximum norm of error after 3 times V cycle=0.00440554

The 4-th V cycle:

The maximum norm of residuals after 4 times V cycle=0.781733

The 4-th residual reduction rate is about 0.972629

The maximum norm of error after 4 times V cycle=0.000162905

The 5-th V cycle:

The maximum norm of residuals after 5 times V cycle=0.0262481

The 5-th residual reduction rate is about 0.966423

The maximum norm of error after 5 times V cycle=5.93768e-06

The 6-th V cycle:

The maximum norm of residuals after 6 times V cycle=0.000799369

The 6-th residual reduction rate is about 0.969546

The maximum norm of error after 6 times V cycle=2.13942e-07

The 7-th V cycle:

The maximum norm of residuals after 7 times V cycle=2.7089e-05

The 7-th residual reduction rate is about 0.966112

The maximum norm of error after 7 times V cycle=7.50504e-09

Obviously, the maximum norm of error has second-order convergence.

\subsection*{III-z n=1025,RO=0,IO=0,cycletype=1}

The maximum norm of residuals and errors is shown below.

The 1-th FMG cycle:
 
The maximum norm of residuals after 1 times FMG cycle=135857

The 1-th residual reduction rate is about 0.972074

The maximum norm of error after 1 times FMG cycle=2.76517

The 2-th FMG cycle:
 
The maximum norm of residuals after 2 times FMG cycle=20391.5

The 2-th residual reduction rate is about 0.849904

The maximum norm of error after 2 times FMG cycle=0.564966

The 3-th FMG cycle:
 
The maximum norm of residuals after 3 times FMG cycle=4741.47

The 3-th residual reduction rate is about 0.767479

The maximum norm of error after 3 times FMG cycle=0.184658

The 4-th FMG cycle:
 
The maximum norm of residuals after 4 times FMG cycle=1445.43

The 4-th residual reduction rate is about 0.695152

The maximum norm of error after 4 times FMG cycle=0.0678655

The 5-th FMG cycle:
 
The maximum norm of residuals after 5 times FMG cycle=452.246

The 5-th residual reduction rate is about 0.687119

The maximum norm of error after 5 times FMG cycle=0.0249565

The 6-th FMG cycle:
 
The maximum norm of residuals after 6 times FMG cycle=144.457

The 6-th residual reduction rate is about 0.680579

The maximum norm of error after 6 times FMG cycle=0.00917577

The 7-th FMG cycle:
 
The maximum norm of residuals after 7 times FMG cycle=46.9081

The 7-th residual reduction rate is about 0.675279

The maximum norm of error after 7 times FMG cycle=0.00337307

The 8-th FMG cycle:
 
The maximum norm of residuals after 8 times FMG cycle=15.4344

The 8-th residual reduction rate is about 0.670965

The maximum norm of error after 8 times FMG cycle=0.00123969

The 9-th FMG cycle:
 
The maximum norm of residuals after 9 times FMG cycle=5.13306

The 9-th residual reduction rate is about 0.667428

The maximum norm of error after 9 times FMG cycle=0.000455643

The 10-th FMG cycle:
 
The maximum norm of residuals after 10 times FMG cycle=1.72212

The 10-th residual reduction rate is about 0.664503

The maximum norm of error after 10 times FMG cycle=0.000167497

The 11-th FMG cycle:
 
The maximum norm of residuals after 11 times FMG cycle=0.58197

The 11-th residual reduction rate is about 0.662063

The maximum norm of error after 11 times FMG cycle=6.15791e-05

The 12-th FMG cycle:
 
The maximum norm of residuals after 12 times FMG cycle=0.197866

The 12-th residual reduction rate is about 0.660006

The maximum norm of error after 12 times FMG cycle=2.26437e-05

The 13-th FMG cycle:
 
The maximum norm of residuals after 13 times FMG cycle=0.0676196

The 13-th residual reduction rate is about 0.658255

The maximum norm of error after 13 times FMG cycle=8.32494e-06

The 14-th FMG cycle:
 
The maximum norm of residuals after 14 times FMG cycle=0.0232105

The 14-th residual reduction rate is about 0.656749

The maximum norm of error after 14 times FMG cycle=3.05937e-06

The 15-th FMG cycle:
 
The maximum norm of residuals after 15 times FMG cycle=0.0079974

The 15-th residual reduction rate is about 0.65544

The maximum norm of error after 15 times FMG cycle=1.12337e-06

The 16-th FMG cycle:
 
The maximum norm of residuals after 16 times FMG cycle=0.00276477

The 16-th residual reduction rate is about 0.654291

The maximum norm of error after 16 times FMG cycle=4.11948e-07

The 17-th FMG cycle:
 
The maximum norm of residuals after 17 times FMG cycle=0.000967609

The 17-th residual reduction rate is about 0.650022

The maximum norm of error after 17 times FMG cycle=1.50798e-07

The 18-th FMG cycle:
 
The maximum norm of residuals after 18 times FMG cycle=0.000339554

The 18-th residual reduction rate is about 0.649079

The maximum norm of error after 18 times FMG cycle=5.50844e-08

The 19-th FMG cycle:
 
The maximum norm of residuals after 19 times FMG cycle=0.000119337

The 19-th residual reduction rate is about 0.648547

The maximum norm of error after 19 times FMG cycle=2.00728e-08

The 20-th FMG cycle:
 
The maximum norm of residuals after 20 times FMG cycle=4.20016e-05

The 20-th residual reduction rate is about 0.648044

The maximum norm of error after 20 times FMG cycle=7.2947e-09

Obviously, the maximum norm of error has the first order convergence.

\subsection*{III-aa n=1025,RO=0,IO=1,cycletype=0}

The maximum norm of residuals and errors is shown below.

The 1-th V cycle:

The maximum norm of residuals after 1 times V cycle=45575.1

The 1-th residual reduction rate is about 0.990632

The maximum norm of error after 1 times V cycle=2.34416

The 2-th V cycle:

The maximum norm of residuals after 2 times V cycle=1033.85

The 2-th residual reduction rate is about 0.977315

The maximum norm of error after 2 times V cycle=0.0269449

The 3-th V cycle:

The maximum norm of residuals after 3 times V cycle=11.0274

The 3-th residual reduction rate is about 0.989334

The maximum norm of error after 3 times V cycle=0.000990246

The 4-th V cycle:

The maximum norm of residuals after 4 times V cycle=0.270778

The 4-th residual reduction rate is about 0.975445

The maximum norm of error after 4 times V cycle=1.69051e-05

The 5-th V cycle:

The maximum norm of residuals after 5 times V cycle=0.00551172

The 5-th residual reduction rate is about 0.979645

The maximum norm of error after 5 times V cycle=3.9964e-07

The 6-th V cycle:

The maximum norm of residuals after 6 times V cycle=0.000116133

The 6-th residual reduction rate is about 0.97893

The maximum norm of error after 6 times V cycle=1.13242e-08

The 7-th V cycle:

The maximum norm of residuals after 7 times V cycle=2.74032e-06

The 7-th residual reduction rate is about 0.976404

The maximum norm of error after 7 times V cycle=1.91094e-10

Obviously, the maximum norm of error has second-order convergence.

\subsection*{III-ab n=1025,RO=0,IO=1,cycletype=1}

The maximum norm of residuals and errors is shown below.

The maximum norm of residuals after 1 times FMG cycle=200574

The 1-th residual reduction rate is about 0.958771

The maximum norm of error after 1 times FMG cycle=3.03522

The 2-th FMG cycle:
 
The maximum norm of residuals after 2 times FMG cycle=46822

The 2-th residual reduction rate is about 0.76656

The maximum norm of error after 2 times FMG cycle=0.947838

The 3-th FMG cycle:
 
The maximum norm of residuals after 3 times FMG cycle=12086.6

The 3-th residual reduction rate is about 0.74186

The maximum norm of error after 3 times FMG cycle=0.328506

The 4-th FMG cycle:
 
The maximum norm of residuals after 4 times FMG cycle=3682.17

The 4-th residual reduction rate is about 0.695352

The maximum norm of error after 4 times FMG cycle=0.138622

The 5-th FMG cycle:
 
The maximum norm of residuals after 5 times FMG cycle=1334.59

The 5-th residual reduction rate is about 0.637553

The maximum norm of error after 5 times FMG cycle=0.0631558

The 6-th FMG cycle:
 
The maximum norm of residuals after 6 times FMG cycle=503.92

The 6-th residual reduction rate is about 0.622416

The maximum norm of error after 6 times FMG cycle=0.0287767

The 7-th FMG cycle:
 
The maximum norm of residuals after 7 times FMG cycle=201.434

The 7-th residual reduction rate is about 0.600265

The maximum norm of error after 7 times FMG cycle=0.0131074

The 8-th FMG cycle:
 
The maximum norm of residuals after 8 times FMG cycle=81.8357

The 8-th residual reduction rate is about 0.593735

The maximum norm of error after 8 times FMG cycle=0.00596636

The 9-th FMG cycle:
 
The maximum norm of residuals after 9 times FMG cycle=33.6901

The 9-th residual reduction rate is about 0.588319

The maximum norm of error after 9 times FMG cycle=0.00271427

The 10-th FMG cycle:
 
The maximum norm of residuals after 10 times FMG cycle=14.0209

The 10-th residual reduction rate is about 0.583828

The maximum norm of error after 10 times FMG cycle=0.00123383

The 11-th FMG cycle:
 
The maximum norm of residuals after 11 times FMG cycle=5.88765

The 11-th residual reduction rate is about 0.58008

The maximum norm of error after 11 times FMG cycle=0.00056048

The 12-th FMG cycle:
 
The maximum norm of residuals after 12 times FMG cycle=2.49095

The 12-th residual reduction rate is about 0.576919

The maximum norm of error after 12 times FMG cycle=0.000254389

The 13-th FMG cycle:
 
The maximum norm of residuals after 13 times FMG cycle=1.0606

The 13-th residual reduction rate is about 0.574218

The maximum norm of error after 13 times FMG cycle=0.00011534

The 14-th FMG cycle:
 
The maximum norm of residuals after 14 times FMG cycle=0.454067

The 14-th residual reduction rate is about 0.571879

The maximum norm of error after 14 times FMG cycle=5.22312e-05

The 15-th FMG cycle:
 
The maximum norm of residuals after 15 times FMG cycle=0.195327

The 15-th residual reduction rate is about 0.569828

The maximum norm of error after 15 times FMG cycle=2.36197e-05

The 16-th FMG cycle:
 
The maximum norm of residuals after 16 times FMG cycle=0.0843798

The 16-th residual reduction rate is about 0.568008

The maximum norm of error after 16 times FMG cycle=1.06627e-05

The 17-th FMG cycle:
 
The maximum norm of residuals after 17 times FMG cycle=0.036589

The 17-th residual reduction rate is about 0.566378

The maximum norm of error after 17 times FMG cycle=4.80437e-06

The 18-th FMG cycle:
 
The maximum norm of residuals after 18 times FMG cycle=0.0159196

The 18-th residual reduction rate is about 0.564906

The maximum norm of error after 18 times FMG cycle=2.16024e-06

The 19-th FMG cycle:
 
The maximum norm of residuals after 19 times FMG cycle=0.00694785

The 19-th residual reduction rate is about 0.563568

The maximum norm of error after 19 times FMG cycle=9.69051e-07

The 20-th FMG cycle:
 
The maximum norm of residuals after 20 times FMG cycle=0.00304076

The 20-th residual reduction rate is about 0.562346

The maximum norm of error after 20 times FMG cycle=4.33591e-07

The 21-th FMG cycle:
 
The maximum norm of residuals after 21 times FMG cycle=0.00133421

The 21-th residual reduction rate is about 0.561224

The maximum norm of error after 21 times FMG cycle=1.93573e-07

The 22-th FMG cycle:
 
The maximum norm of residuals after 22 times FMG cycle=0.000586795

The 22-th residual reduction rate is about 0.560193

The maximum norm of error after 22 times FMG cycle=8.61753e-08

The 23-th FMG cycle:
 
The maximum norm of residuals after 23 times FMG cycle=0.000258636

The 23-th residual reduction rate is about 0.559241

The maximum norm of error after 23 times FMG cycle=3.82692e-08

The 24-th FMG cycle:
 
The maximum norm of residuals after 24 times FMG cycle=0.000114224

The 24-th residual reduction rate is about 0.558359

The maximum norm of error after 24 times FMG cycle=1.69493e-08

The 25-th FMG cycle:
 
The maximum norm of residuals after 25 times FMG cycle=5.0539e-05

The 25-th residual reduction rate is about 0.557545

The maximum norm of error after 25 times FMG cycle=7.48786e-09

Obviously, the maximum norm of error has the first order convergence.

\subsection*{III-ac n=1025,RO=1,IO=0,cycletype=0}

The maximum norm of residuals and errors is shown below.

The 1-th V cycle:

The maximum norm of residuals after 1 times V cycle=156045

The 1-th residual reduction rate is about 0.967924

The maximum norm of error after 1 times V cycle=1.95991

The 2-th V cycle:

The maximum norm of residuals after 2 times V cycle=10709.2

The 2-th residual reduction rate is about 0.931371

The maximum norm of error after 2 times V cycle=2.16432

The 3-th V cycle:

The maximum norm of residuals after 3 times V cycle=836.734

The 3-th residual reduction rate is about 0.921867

The maximum norm of error after 3 times V cycle=0.124433

The 4-th V cycle:

The maximum norm of residuals after 4 times V cycle=84.5041

The 4-th residual reduction rate is about 0.899007

The maximum norm of error after 4 times V cycle=0.0535194

The 5-th V cycle:

The maximum norm of residuals after 5 times V cycle=7.18527

The 5-th residual reduction rate is about 0.914971

The maximum norm of error after 5 times V cycle=0.00489654

The 6-th V cycle:

The maximum norm of residuals after 6 times V cycle=0.754454

The 6-th residual reduction rate is about 0.895

The maximum norm of error after 6 times V cycle=0.000953872

The 7-th V cycle:

The maximum norm of residuals after 7 times V cycle=0.0765545

The 7-th residual reduction rate is about 0.89853

The maximum norm of error after 7 times V cycle=0.000113467

The 8-th V cycle:

The maximum norm of residuals after 8 times V cycle=0.00830413

The 8-th residual reduction rate is about 0.891527

The maximum norm of error after 8 times V cycle=1.57088e-05

The 9-th V cycle:

The maximum norm of residuals after 9 times V cycle=0.000732033

The 9-th residual reduction rate is about 0.911847

The maximum norm of error after 9 times V cycle=2.35633e-06

The 10-th V cycle:

The maximum norm of residuals after 10 times V cycle=9.06342e-05

The 10-th residual reduction rate is about 0.876188

The maximum norm of error after 10 times V cycle=2.59107e-07

The 11-th V cycle:

The maximum norm of residuals after 11 times V cycle=8.55727e-06

The 11-th residual reduction rate is about 0.905585

The maximum norm of error after 11 times V cycle=3.94702e-08

The 12-th V cycle:

The maximum norm of residuals after 12 times V cycle=1.00978e-06

The 12-th residual reduction rate is about 0.881997

The maximum norm of error after 12 times V cycle=4.14369e-09

Obviously, the maximum norm of error has second-order convergence.

\subsection*{III-ad n=1025,RO=1,IO=0,cycletype=1}

The maximum norm of residuals and errors is shown below.

The 1-th FMG cycle:
 
The maximum norm of residuals after 1 times FMG cycle=228043

The 1-th residual reduction rate is about 0.953125

The maximum norm of error after 1 times FMG cycle=1.68553

The 2-th FMG cycle:
 
The maximum norm of residuals after 2 times FMG cycle=80124.7

The 2-th residual reduction rate is about 0.648642

The maximum norm of error after 2 times FMG cycle=2.41453

The 3-th FMG cycle:
 
The maximum norm of residuals after 3 times FMG cycle=43792.6

The 3-th residual reduction rate is about 0.453444

The maximum norm of error after 3 times FMG cycle=2.93381

The 4-th FMG cycle:
 
The maximum norm of residuals after 4 times FMG cycle=29492.1

The 4-th residual reduction rate is about 0.32655

The maximum norm of error after 4 times FMG cycle=4.22954

The 5-th FMG cycle:
 
The maximum norm of residuals after 5 times FMG cycle=18035.4

The 5-th residual reduction rate is about 0.388469

The maximum norm of error after 5 times FMG cycle=5.10524

The 6-th FMG cycle:
 
The maximum norm of residuals after 6 times FMG cycle=15751.8

The 6-th residual reduction rate is about 0.126614

The maximum norm of error after 6 times FMG cycle=8.97778

The 7-th FMG cycle:
 
The maximum norm of residuals after 7 times FMG cycle=12102.1

The 7-th residual reduction rate is about 0.231702

The maximum norm of error after 7 times FMG cycle=10.4002

The 8-th FMG cycle:
 
The maximum norm of residuals after 8 times FMG cycle=8521.9

The 8-th residual reduction rate is about 0.295833

The maximum norm of error after 8 times FMG cycle=9.0708

The 9-th FMG cycle:
 
The maximum norm of residuals after 9 times FMG cycle=5640.76

The 9-th residual reduction rate is about 0.338086

The maximum norm of error after 9 times FMG cycle=5.47435

The 10-th FMG cycle:
 
The maximum norm of residuals after 10 times FMG cycle=3670.41

The 10-th residual reduction rate is about 0.349306

The maximum norm of error after 10 times FMG cycle=4.04676

The 11-th FMG cycle:
 
The maximum norm of residuals after 11 times FMG cycle=2714.59

The 11-th residual reduction rate is about 0.260412

The maximum norm of error after 11 times FMG cycle=8.30588

The 12-th FMG cycle:
 
The maximum norm of residuals after 12 times FMG cycle=2272.26

The 12-th residual reduction rate is about 0.162946

The maximum norm of error after 12 times FMG cycle=10.7603

The 13-th FMG cycle:
 
The maximum norm of residuals after 13 times FMG cycle=2119.76

The 13-th residual reduction rate is about 0.0671108

The maximum norm of error after 13 times FMG cycle=11.1039

The 14-th FMG cycle:
 
The maximum norm of residuals after 14 times FMG cycle=1802.06

The 14-th residual reduction rate is about 0.149876

The maximum norm of error after 14 times FMG cycle=9.84901

The 15-th FMG cycle:
 
The maximum norm of residuals after 15 times FMG cycle=1426.28

The 15-th residual reduction rate is about 0.20853

The maximum norm of error after 15 times FMG cycle=7.73294

The 16-th FMG cycle:
 
The maximum norm of residuals after 16 times FMG cycle=1065.24

The 16-th residual reduction rate is about 0.253133

The maximum norm of error after 16 times FMG cycle=5.42473

The 17-th FMG cycle:
 
The maximum norm of residuals after 17 times FMG cycle=807.921

The 17-th residual reduction rate is about 0.24156

The maximum norm of error after 17 times FMG cycle=3.88425

The 18-th FMG cycle:
 
The maximum norm of residuals after 18 times FMG cycle=620.902

The 18-th residual reduction rate is about 0.231481

The maximum norm of error after 18 times FMG cycle=2.97377

The 19-th FMG cycle:
 
The maximum norm of residuals after 19 times FMG cycle=453.375

The 19-th residual reduction rate is about 0.269812

The maximum norm of error after 19 times FMG cycle=2.2691

The 20-th FMG cycle:
 
The maximum norm of residuals after 20 times FMG cycle=314.968

The 20-th residual reduction rate is about 0.305282

The maximum norm of error after 20 times FMG cycle=1.65041

The 21-th FMG cycle:
 
The maximum norm of residuals after 21 times FMG cycle=238.505

The 21-th residual reduction rate is about 0.242765

The maximum norm of error after 21 times FMG cycle=1.26324

The 22-th FMG cycle:
 
The maximum norm of residuals after 22 times FMG cycle=184.103

The 22-th residual reduction rate is about 0.228096

The maximum norm of error after 22 times FMG cycle=1.3402

The 23-th FMG cycle:
 
The maximum norm of residuals after 23 times FMG cycle=137.949

The 23-th residual reduction rate is about 0.250696

The maximum norm of error after 23 times FMG cycle=1.36128

The 24-th FMG cycle:
 
The maximum norm of residuals after 24 times FMG cycle=100.552

The 24-th residual reduction rate is about 0.271096

The maximum norm of error after 24 times FMG cycle=1.52962

The 25-th FMG cycle:
 
The maximum norm of residuals after 25 times FMG cycle=87.2181

The 25-th residual reduction rate is about 0.132604

The maximum norm of error after 25 times FMG cycle=1.65259

The 26-th FMG cycle:
 
The maximum norm of residuals after 26 times FMG cycle=75.8202

The 26-th residual reduction rate is about 0.130683

The maximum norm of error after 26 times FMG cycle=1.69759

The 27-th FMG cycle:
 
The maximum norm of residuals after 27 times FMG cycle=64.2741

The 27-th residual reduction rate is about 0.152282

The maximum norm of error after 27 times FMG cycle=1.66076

The 28-th FMG cycle:
 
The maximum norm of residuals after 28 times FMG cycle=53.139

The 28-th residual reduction rate is about 0.173244

The maximum norm of error after 28 times FMG cycle=1.54876

The 29-th FMG cycle:
 
The maximum norm of residuals after 29 times FMG cycle=42.8156

The 29-th residual reduction rate is about 0.194273

The maximum norm of error after 29 times FMG cycle=1.37786

The 30-th FMG cycle:
 
The maximum norm of residuals after 30 times FMG cycle=33.5754

The 30-th residual reduction rate is about 0.215812

The maximum norm of error after 30 times FMG cycle=1.17045

The 31-th FMG cycle:
 
The maximum norm of residuals after 31 times FMG cycle=25.5771

The 31-th residual reduction rate is about 0.238221

The maximum norm of error after 31 times FMG cycle=0.950097

The 32-th FMG cycle:
 
The maximum norm of residuals after 32 times FMG cycle=18.878

The 32-th residual reduction rate is about 0.261916

The maximum norm of error after 32 times FMG cycle=0.737301

The 33-th FMG cycle:
 
The maximum norm of residuals after 33 times FMG cycle=14.2649

The 33-th residual reduction rate is about 0.244363

The maximum norm of error after 33 times FMG cycle=0.546943

The 34-th FMG cycle:
 
The maximum norm of residuals after 34 times FMG cycle=10.7532

The 34-th residual reduction rate is about 0.246177

The maximum norm of error after 34 times FMG cycle=0.387482

The 35-th FMG cycle:
 
The maximum norm of residuals after 35 times FMG cycle=7.88575

The 35-th residual reduction rate is about 0.266661

The maximum norm of error after 35 times FMG cycle=0.261579

The 36-th FMG cycle:
 
The maximum norm of residuals after 36 times FMG cycle=5.62007

The 36-th residual reduction rate is about 0.287313

The maximum norm of error after 36 times FMG cycle=0.167587

The 37-th FMG cycle:
 
The maximum norm of residuals after 37 times FMG cycle=3.88625

The 37-th residual reduction rate is about 0.308505

The maximum norm of error after 37 times FMG cycle=0.101306

The 38-th FMG cycle:
 
The maximum norm of residuals after 38 times FMG cycle=2.60082

The 38-th residual reduction rate is about 0.330764

The maximum norm of error after 38 times FMG cycle=0.0572164

The 39-th FMG cycle:
 
The maximum norm of residuals after 39 times FMG cycle=1.86946

The 39-th residual reduction rate is about 0.281202

The maximum norm of error after 39 times FMG cycle=0.0332642

The 40-th FMG cycle:
 
The maximum norm of residuals after 40 times FMG cycle=1.46536

The 40-th residual reduction rate is about 0.216161

The maximum norm of error after 40 times FMG cycle=0.02687

The 41-th FMG cycle:
 
The maximum norm of residuals after 41 times FMG cycle=1.12675

The 41-th residual reduction rate is about 0.231074

The maximum norm of error after 41 times FMG cycle=0.0195627

The 42-th FMG cycle:
 
The maximum norm of residuals after 42 times FMG cycle=0.849221

The 42-th residual reduction rate is about 0.24631

The maximum norm of error after 42 times FMG cycle=0.0124693

The 43-th FMG cycle:
 
The maximum norm of residuals after 43 times FMG cycle=0.626162

The 43-th residual reduction rate is about 0.262663

The maximum norm of error after 43 times FMG cycle=0.00628507

The 44-th FMG cycle:
 
The maximum norm of residuals after 44 times FMG cycle=0.460847

The 44-th residual reduction rate is about 0.264014

The maximum norm of error after 44 times FMG cycle=0.00390581

The 45-th FMG cycle:
 
The maximum norm of residuals after 45 times FMG cycle=0.330712

The 45-th residual reduction rate is about 0.282381

The maximum norm of error after 45 times FMG cycle=0.00526001

The 46-th FMG cycle:
 
The maximum norm of residuals after 46 times FMG cycle=0.247888

The 46-th residual reduction rate is about 0.250441

The maximum norm of error after 46 times FMG cycle=0.00626978

The 47-th FMG cycle:
 
The maximum norm of residuals after 47 times FMG cycle=0.207046

The 47-th residual reduction rate is about 0.164761

The maximum norm of error after 47 times FMG cycle=0.00680756

The 48-th FMG cycle:
 
The maximum norm of residuals after 48 times FMG cycle=0.175853

The 48-th residual reduction rate is about 0.150657

The maximum norm of error after 48 times FMG cycle=0.00709719

The 49-th FMG cycle:
 
The maximum norm of residuals after 49 times FMG cycle=0.151351

The 49-th residual reduction rate is about 0.13933

The maximum norm of error after 49 times FMG cycle=0.00698157

The 50-th FMG cycle:
 
The maximum norm of residuals after 50 times FMG cycle=0.128846

The 50-th residual reduction rate is about 0.148697

The maximum norm of error after 50 times FMG cycle=0.0065168

The 51-th FMG cycle:
 
The maximum norm of residuals after 51 times FMG cycle=0.107308

The 51-th residual reduction rate is about 0.167156

The maximum norm of error after 51 times FMG cycle=0.0058429

The 52-th FMG cycle:
 
The maximum norm of residuals after 52 times FMG cycle=0.0874483

The 52-th residual reduction rate is about 0.185075

The maximum norm of error after 52 times FMG cycle=0.0050699

The 53-th FMG cycle:
 
The maximum norm of residuals after 53 times FMG cycle=0.0697092

The 53-th residual reduction rate is about 0.202852

The maximum norm of error after 53 times FMG cycle=0.00427732

The 54-th FMG cycle:
 
The maximum norm of residuals after 54 times FMG cycle=0.0543925

The 54-th residual reduction rate is about 0.219724

The maximum norm of error after 54 times FMG cycle=0.00351844

The 55-th FMG cycle:
 
The maximum norm of residuals after 55 times FMG cycle=0.0446877

The 55-th residual reduction rate is about 0.17842

The maximum norm of error after 55 times FMG cycle=0.00282557

The 56-th FMG cycle:
 
The maximum norm of residuals after 56 times FMG cycle=0.0371055

The 56-th residual reduction rate is about 0.169673

The maximum norm of error after 56 times FMG cycle=0.00221563

The 57-th FMG cycle:
 
The maximum norm of residuals after 57 times FMG cycle=0.0299765

The 57-th residual reduction rate is about 0.192126

The maximum norm of error after 57 times FMG cycle=0.00169463

The 58-th FMG cycle:
 
The maximum norm of residuals after 58 times FMG cycle=0.0235876

The 58-th residual reduction rate is about 0.213132

The maximum norm of error after 58 times FMG cycle=0.00126143

The 59-th FMG cycle:
 
The maximum norm of residuals after 59 times FMG cycle=0.0180762

The 59-th residual reduction rate is about 0.233657

The maximum norm of error after 59 times FMG cycle=0.000910269

The 60-th FMG cycle:
 
The maximum norm of residuals after 60 times FMG cycle=0.0134849

The 60-th residual reduction rate is about 0.253995

The maximum norm of error after 60 times FMG cycle=0.000632754

The 61-th FMG cycle:
 
The maximum norm of residuals after 61 times FMG cycle=0.00977452

The 61-th residual reduction rate is about 0.275152

The maximum norm of error after 61 times FMG cycle=0.000419242

The 62-th FMG cycle:
 
The maximum norm of residuals after 62 times FMG cycle=0.00707651

The 62-th residual reduction rate is about 0.276025

The maximum norm of error after 62 times FMG cycle=0.000259748

The 63-th FMG cycle:
 
The maximum norm of residuals after 63 times FMG cycle=0.00495248

The 63-th residual reduction rate is about 0.300151

The maximum norm of error after 63 times FMG cycle=0.000144599

The 64-th FMG cycle:
 
The maximum norm of residuals after 64 times FMG cycle=0.00332102

The 64-th residual reduction rate is about 0.329422

The maximum norm of error after 64 times FMG cycle=6.49961e-05

The 65-th FMG cycle:
 
The maximum norm of residuals after 65 times FMG cycle=0.00254159

The 65-th residual reduction rate is about 0.234698

The maximum norm of error after 65 times FMG cycle=2.02829e-05

The 66-th FMG cycle:
 
The maximum norm of residuals after 66 times FMG cycle=0.00197695

The 66-th residual reduction rate is about 0.222159

The maximum norm of error after 66 times FMG cycle=2.8533e-05

The 67-th FMG cycle:
 
The maximum norm of residuals after 67 times FMG cycle=0.00149422

The 67-th residual reduction rate is about 0.244179

The maximum norm of error after 67 times FMG cycle=3.6688e-05

The 68-th FMG cycle:
 
The maximum norm of residuals after 68 times FMG cycle=0.0011329

The 68-th residual reduction rate is about 0.24181

The maximum norm of error after 68 times FMG cycle=4.30957e-05

The 69-th FMG cycle:
 
The maximum norm of residuals after 69 times FMG cycle=0.000972244

The 69-th residual reduction rate is about 0.141812

The maximum norm of error after 69 times FMG cycle=4.32491e-05

The 70-th FMG cycle:
 
The maximum norm of residuals after 70 times FMG cycle=0.000799861

The 70-th residual reduction rate is about 0.177304

The maximum norm of error after 70 times FMG cycle=3.94853e-05

The 71-th FMG cycle:
 
The maximum norm of residuals after 71 times FMG cycle=0.000642356

The 71-th residual reduction rate is about 0.196915

The maximum norm of error after 71 times FMG cycle=3.37459e-05

The 72-th FMG cycle:
 
The maximum norm of residuals after 72 times FMG cycle=0.000495172

The 72-th residual reduction rate is about 0.229132

The maximum norm of error after 72 times FMG cycle=2.73563e-05

The 73-th FMG cycle:
 
The maximum norm of residuals after 73 times FMG cycle=0.000395976

The 73-th residual reduction rate is about 0.200328

The maximum norm of error after 73 times FMG cycle=2.11599e-05

The 74-th FMG cycle:
 
The maximum norm of residuals after 74 times FMG cycle=0.00030448

The 74-th residual reduction rate is about 0.231063

The maximum norm of error after 74 times FMG cycle=1.56369e-05

The 75-th FMG cycle:
 
The maximum norm of residuals after 75 times FMG cycle=0.000224867

The 75-th residual reduction rate is about 0.261472

The maximum norm of error after 75 times FMG cycle=1.10108e-05

The 76-th FMG cycle:
 
The maximum norm of residuals after 76 times FMG cycle=0.000172555

The 76-th residual reduction rate is about 0.232633

The maximum norm of error after 76 times FMG cycle=7.33142e-06

The 77-th FMG cycle:
 
The maximum norm of residuals after 77 times FMG cycle=0.000133262

The 77-th residual reduction rate is about 0.227717

The maximum norm of error after 77 times FMG cycle=4.54197e-06

The 78-th FMG cycle:
 
The maximum norm of residuals after 78 times FMG cycle=0.00011339

The 78-th residual reduction rate is about 0.14912

The maximum norm of error after 78 times FMG cycle=2.52723e-06

The 79-th FMG cycle:
 
The maximum norm of residuals after 79 times FMG cycle=9.72248e-05

The 79-th residual reduction rate is about 0.142559

The maximum norm of error after 79 times FMG cycle=1.14999e-06

The 80-th FMG cycle:
 
The maximum norm of residuals after 80 times FMG cycle=8.03672e-05

The 80-th residual reduction rate is about 0.173388

The maximum norm of error after 80 times FMG cycle=5.50266e-07

The 81-th FMG cycle:
 
The maximum norm of residuals after 81 times FMG cycle=6.42085e-05

The 81-th residual reduction rate is about 0.201061

The maximum norm of error after 81 times FMG cycle=7.08969e-07

The 82-th FMG cycle:
 
The maximum norm of residuals after 82 times FMG cycle=4.99483e-05

The 82-th residual reduction rate is about 0.222091

The maximum norm of error after 82 times FMG cycle=7.54081e-07

The 83-th FMG cycle:
 
The maximum norm of residuals after 83 times FMG cycle=3.77413e-05

The 83-th residual reduction rate is about 0.244394

The maximum norm of error after 83 times FMG cycle=7.09214e-07

The 84-th FMG cycle:
 
The maximum norm of residuals after 84 times FMG cycle=2.74737e-05

The 84-th residual reduction rate is about 0.272052

The maximum norm of error after 84 times FMG cycle=6.21625e-07

The 85-th FMG cycle:
 
The maximum norm of residuals after 85 times FMG cycle=1.91469e-05

The 85-th residual reduction rate is about 0.30308

The maximum norm of error after 85 times FMG cycle=5.36685e-07

The 86-th FMG cycle:
 
The maximum norm of residuals after 86 times FMG cycle=1.38516e-05

The 86-th residual reduction rate is about 0.276561

The maximum norm of error after 86 times FMG cycle=4.29413e-07

The 87-th FMG cycle:
 
The maximum norm of residuals after 87 times FMG cycle=9.89754e-06

The 87-th residual reduction rate is about 0.285461

The maximum norm of error after 87 times FMG cycle=3.20684e-07

The 88-th FMG cycle:
 
The maximum norm of residuals after 88 times FMG cycle=7.74104e-06

The 88-th residual reduction rate is about 0.217882

The maximum norm of error after 88 times FMG cycle=2.2254e-07

The 89-th FMG cycle:
 
The maximum norm of residuals after 89 times FMG cycle=6.23252e-06

The 89-th residual reduction rate is about 0.194873

The maximum norm of error after 89 times FMG cycle=1.4071e-07

The 90-th FMG cycle:
 
The maximum norm of residuals after 90 times FMG cycle=4.86931e-06

The 90-th residual reduction rate is about 0.218725

The maximum norm of error after 90 times FMG cycle=7.71057e-08

The 91-th FMG cycle:
 
The maximum norm of residuals after 91 times FMG cycle=3.98276e-06

The 91-th residual reduction rate is about 0.182069

The maximum norm of error after 91 times FMG cycle=3.11159e-08

The 92-th FMG cycle:
 
The maximum norm of residuals after 92 times FMG cycle=3.33812e-06

The 92-th residual reduction rate is about 0.161857

The maximum norm of error after 92 times FMG cycle=4.16006e-08

The 93-th FMG cycle:
 
The maximum norm of residuals after 93 times FMG cycle=2.70476e-06

The 93-th residual reduction rate is about 0.189735

The maximum norm of error after 93 times FMG cycle=5.045e-08

The 94-th FMG cycle:
 
The maximum norm of residuals after 94 times FMG cycle=2.11716e-06

The 94-th residual reduction rate is about 0.217248

The maximum norm of error after 94 times FMG cycle=5.2729e-08

The 95-th FMG cycle:
 
The maximum norm of residuals after 95 times FMG cycle=1.65602e-06

The 95-th residual reduction rate is about 0.21781

The maximum norm of error after 95 times FMG cycle=5.0515e-08

The 96-th FMG cycle:
 
The maximum norm of residuals after 96 times FMG cycle=1.40617e-06

The 96-th residual reduction rate is about 0.150875

The maximum norm of error after 96 times FMG cycle=4.5419e-08

The 97-th FMG cycle:
 
The maximum norm of residuals after 97 times FMG cycle=1.14472e-06

The 97-th residual reduction rate is about 0.185927

The maximum norm of error after 97 times FMG cycle=3.89077e-08

The 98-th FMG cycle:
 
The maximum norm of residuals after 98 times FMG cycle=8.98132e-07

The 98-th residual reduction rate is about 0.215416

The maximum norm of error after 98 times FMG cycle=3.20301e-08

The 99-th FMG cycle:
 
The maximum norm of residuals after 99 times FMG cycle=6.78597e-07

The 99-th residual reduction rate is about 0.244435

The maximum norm of error after 99 times FMG cycle=2.57074e-08

The 100-th FMG cycle:
 
The maximum norm of residuals after 100 times FMG cycle=4.93947e-07

The 100-th residual reduction rate is about 0.272106

The maximum norm of error after 100 times FMG cycle=2.00808e-08

Obviously, the maximum norm of error has the first order convergence.

\subsection*{III-ae n=1025,RO=1,IO=1,cycletype=0}

The maximum norm of residuals and errors is shown below.

The 1-th V cycle:

The maximum norm of residuals after 1 times V cycle=115719

The 1-th residual reduction rate is about 0.976214

The maximum norm of error after 1 times V cycle=1.99496

The 2-th V cycle:

The maximum norm of residuals after 2 times V cycle=5986.8

The 2-th residual reduction rate is about 0.948264

The maximum norm of error after 2 times V cycle=2.32591

The 3-th V cycle:

The maximum norm of residuals after 3 times V cycle=380.89

The 3-th residual reduction rate is about 0.936378

The maximum norm of error after 3 times V cycle=0.23927

The 4-th V cycle:

The maximum norm of residuals after 4 times V cycle=17.9382

The 4-th residual reduction rate is about 0.952904

The maximum norm of error after 4 times V cycle=0.0102894

The 5-th V cycle:

The maximum norm of residuals after 5 times V cycle=1.42643

The 5-th residual reduction rate is about 0.920481

The maximum norm of error after 5 times V cycle=0.00024135

The 6-th V cycle:

The maximum norm of residuals after 6 times V cycle=0.0634455

The 6-th residual reduction rate is about 0.955521

The maximum norm of error after 6 times V cycle=6.08532e-05

The 7-th V cycle:

The maximum norm of residuals after 7 times V cycle=0.00373547

The 7-th residual reduction rate is about 0.941123

The maximum norm of error after 7 times V cycle=3.98901e-06

The 8-th V cycle:

The maximum norm of residuals after 8 times V cycle=0.000333315

The 8-th residual reduction rate is about 0.91077

The maximum norm of error after 8 times V cycle=1.59494e-07

The 9-th V cycle:

The maximum norm of residuals after 9 times V cycle=1.7626e-05

The 9-th residual reduction rate is about 0.947119

The maximum norm of error after 9 times V cycle=1.20177e-08

The 10-th V cycle:

The maximum norm of residuals after 10 times V cycle=1.34846e-06

The 10-th residual reduction rate is about 0.923496

The maximum norm of error after 10 times V cycle=1.6237e-09

Obviously, the maximum norm of error has second-order convergence.

\subsection*{III-af n=1025,RO=1,IO=1,cycletype=1}

The maximum norm of residuals and errors is shown below.

The 1-th FMG cycle:
 
The maximum norm of residuals after 1 times FMG cycle=228043

The 1-th residual reduction rate is about 0.953125

The maximum norm of error after 1 times FMG cycle=1.68553

The 2-th FMG cycle:
 
The maximum norm of residuals after 2 times FMG cycle=86612.5

The 2-th residual reduction rate is about 0.620192

The maximum norm of error after 2 times FMG cycle=2.58562

The 3-th FMG cycle:
 
The maximum norm of residuals after 3 times FMG cycle=39532.9

The 3-th residual reduction rate is about 0.543566

The maximum norm of error after 3 times FMG cycle=2.89094

The 4-th FMG cycle:
 
The maximum norm of residuals after 4 times FMG cycle=20440.6

The 4-th residual reduction rate is about 0.482948

The maximum norm of error after 4 times FMG cycle=3.72777

The 5-th FMG cycle:
 
The maximum norm of residuals after 5 times FMG cycle=9545.15

The 5-th residual reduction rate is about 0.53303

The maximum norm of error after 5 times FMG cycle=4.37941

The 6-th FMG cycle:
 
The maximum norm of residuals after 6 times FMG cycle=4743.87

The 6-th residual reduction rate is about 0.503007

The maximum norm of error after 6 times FMG cycle=6.87016

The 7-th FMG cycle:
 
The maximum norm of residuals after 7 times FMG cycle=2684.35

The 7-th residual reduction rate is about 0.434143

The maximum norm of error after 7 times FMG cycle=7.16302

The 8-th FMG cycle:
 
The maximum norm of residuals after 8 times FMG cycle=1464.45

The 8-th residual reduction rate is about 0.454451

The maximum norm of error after 8 times FMG cycle=5.63247

The 9-th FMG cycle:
 
The maximum norm of residuals after 9 times FMG cycle=988.037

The 9-th residual reduction rate is about 0.325316

The maximum norm of error after 9 times FMG cycle=3.57152

The 10-th FMG cycle:
 
The maximum norm of residuals after 10 times FMG cycle=675.475

The 10-th residual reduction rate is about 0.316347

The maximum norm of error after 10 times FMG cycle=3.2617

The 11-th FMG cycle:
 
The maximum norm of residuals after 11 times FMG cycle=415.123

The 11-th residual reduction rate is about 0.385435

The maximum norm of error after 11 times FMG cycle=3.10168

The 12-th FMG cycle:
 
The maximum norm of residuals after 12 times FMG cycle=233.705

The 12-th residual reduction rate is about 0.437023

The maximum norm of error after 12 times FMG cycle=2.69526

The 13-th FMG cycle:
 
The maximum norm of residuals after 13 times FMG cycle=134.447

The 13-th residual reduction rate is about 0.424715

The maximum norm of error after 13 times FMG cycle=2.19946

The 14-th FMG cycle:
 
The maximum norm of residuals after 14 times FMG cycle=76.1669

The 14-th residual reduction rate is about 0.433479

The maximum norm of error after 14 times FMG cycle=1.7143

The 15-th FMG cycle:
 
The maximum norm of residuals after 15 times FMG cycle=43.9327

The 15-th residual reduction rate is about 0.423205

The maximum norm of error after 15 times FMG cycle=1.34159

The 16-th FMG cycle:
 
The maximum norm of residuals after 16 times FMG cycle=27.1262

The 16-th residual reduction rate is about 0.38255

The maximum norm of error after 16 times FMG cycle=1.03892

The 17-th FMG cycle:
 
The maximum norm of residuals after 17 times FMG cycle=18.0065

The 17-th residual reduction rate is about 0.336197

The maximum norm of error after 17 times FMG cycle=0.781152

The 18-th FMG cycle:
 
The maximum norm of residuals after 18 times FMG cycle=11.4787

The 18-th residual reduction rate is about 0.362527

The maximum norm of error after 18 times FMG cycle=0.574774

The 19-th FMG cycle:
 
The maximum norm of residuals after 19 times FMG cycle=6.96409

The 19-th residual reduction rate is about 0.393301

The maximum norm of error after 19 times FMG cycle=0.416472

The 20-th FMG cycle:
 
The maximum norm of residuals after 20 times FMG cycle=4.16526

The 20-th residual reduction rate is about 0.401894

The maximum norm of error after 20 times FMG cycle=0.298346

The 21-th FMG cycle:
 
The maximum norm of residuals after 21 times FMG cycle=2.82193

The 21-th residual reduction rate is about 0.322508

The maximum norm of error after 21 times FMG cycle=0.211691

The 22-th FMG cycle:
 
The maximum norm of residuals after 22 times FMG cycle=2.02349

The 22-th residual reduction rate is about 0.282943

The maximum norm of error after 22 times FMG cycle=0.148824

The 23-th FMG cycle:
 
The maximum norm of residuals after 23 times FMG cycle=1.42118

The 23-th residual reduction rate is about 0.29766

The maximum norm of error after 23 times FMG cycle=0.103614

The 24-th FMG cycle:
 
The maximum norm of residuals after 24 times FMG cycle=0.978928

The 24-th residual reduction rate is about 0.311184

The maximum norm of error after 24 times FMG cycle=0.0713877

The 25-th FMG cycle:
 
The maximum norm of residuals after 25 times FMG cycle=0.660101

The 25-th residual reduction rate is about 0.32569

The maximum norm of error after 25 times FMG cycle=0.0486484

The 26-th FMG cycle:
 
The maximum norm of residuals after 26 times FMG cycle=0.43589

The 26-th residual reduction rate is about 0.339662

The maximum norm of error after 26 times FMG cycle=0.0327901

The 27-th FMG cycle:
 
The maximum norm of residuals after 27 times FMG cycle=0.282271

The 27-th residual reduction rate is about 0.352426

The maximum norm of error after 27 times FMG cycle=0.0218729

The 28-th FMG cycle:
 
The maximum norm of residuals after 28 times FMG cycle=0.179546

The 28-th residual reduction rate is about 0.363925

The maximum norm of error after 28 times FMG cycle=0.0144581

The 29-th FMG cycle:
 
The maximum norm of residuals after 29 times FMG cycle=0.113209

The 29-th residual reduction rate is about 0.36947

The maximum norm of error after 29 times FMG cycle=0.00948825

The 30-th FMG cycle:
 
The maximum norm of residuals after 30 times FMG cycle=0.0720004

The 30-th residual reduction rate is about 0.364004

The maximum norm of error after 30 times FMG cycle=0.00619752

The 31-th FMG cycle:
 
The maximum norm of residuals after 31 times FMG cycle=0.0452824

The 31-th residual reduction rate is about 0.37108

The maximum norm of error after 31 times FMG cycle=0.00404084

The 32-th FMG cycle:
 
The maximum norm of residuals after 32 times FMG cycle=0.0284444

The 32-th residual reduction rate is about 0.371845

The maximum norm of error after 32 times FMG cycle=0.00263802

The 33-th FMG cycle:
 
The maximum norm of residuals after 33 times FMG cycle=0.0177966

The 33-th residual reduction rate is about 0.374336

The maximum norm of error after 33 times FMG cycle=0.00172939

The 34-th FMG cycle:
 
The maximum norm of residuals after 34 times FMG cycle=0.0111206

The 34-th residual reduction rate is about 0.375125

The maximum norm of error after 34 times FMG cycle=0.00114104

The 35-th FMG cycle:
 
The maximum norm of residuals after 35 times FMG cycle=0.00693129

The 35-th residual reduction rate is about 0.376719

The maximum norm of error after 35 times FMG cycle=0.000758719

The 36-th FMG cycle:
 
The maximum norm of residuals after 36 times FMG cycle=0.00452312

The 36-th residual reduction rate is about 0.347435

The maximum norm of error after 36 times FMG cycle=0.000508562

The 37-th FMG cycle:
 
The maximum norm of residuals after 37 times FMG cycle=0.00324476

The 37-th residual reduction rate is about 0.282628

The maximum norm of error after 37 times FMG cycle=0.000343322

The 38-th FMG cycle:
 
The maximum norm of residuals after 38 times FMG cycle=0.00229824

The 38-th residual reduction rate is about 0.291706

The maximum norm of error after 38 times FMG cycle=0.000233124

The 39-th FMG cycle:
 
The maximum norm of residuals after 39 times FMG cycle=0.00160939

The 39-th residual reduction rate is about 0.299729

The maximum norm of error after 39 times FMG cycle=0.000159236

The 40-th FMG cycle:
 
The maximum norm of residuals after 40 times FMG cycle=0.00111528

The 40-th residual reduction rate is about 0.307019

The maximum norm of error after 40 times FMG cycle=0.000109037

The 41-th FMG cycle:
 
The maximum norm of residuals after 41 times FMG cycle=0.000765176

The 41-th residual reduction rate is about 0.313914

The maximum norm of error after 41 times FMG cycle=7.4417e-05

The 42-th FMG cycle:
 
The maximum norm of residuals after 42 times FMG cycle=0.000519973

The 42-th residual reduction rate is about 0.320453

The maximum norm of error after 42 times FMG cycle=5.04943e-05

The 43-th FMG cycle:
 
The maximum norm of residuals after 43 times FMG cycle=0.000350222

The 43-th residual reduction rate is about 0.326462

The maximum norm of error after 43 times FMG cycle=3.40251e-05

The 44-th FMG cycle:
 
The maximum norm of residuals after 44 times FMG cycle=0.00023399

The 44-th residual reduction rate is about 0.331882

The maximum norm of error after 44 times FMG cycle=2.27624e-05

The 45-th FMG cycle:
 
The maximum norm of residuals after 45 times FMG cycle=0.000155171

The 45-th residual reduction rate is about 0.336847

The maximum norm of error after 45 times FMG cycle=1.51178e-05

The 46-th FMG cycle:
 
The maximum norm of residuals after 46 times FMG cycle=0.000102176

The 46-th residual reduction rate is about 0.341524

The maximum norm of error after 46 times FMG cycle=9.96963e-06

The 47-th FMG cycle:
 
The maximum norm of residuals after 47 times FMG cycle=6.68448e-05

The 47-th residual reduction rate is about 0.34579

The maximum norm of error after 47 times FMG cycle=6.53001e-06

The 48-th FMG cycle:
 
The maximum norm of residuals after 48 times FMG cycle=4.34713e-05

The 48-th residual reduction rate is about 0.349668

The maximum norm of error after 48 times FMG cycle=4.24962e-06

The 49-th FMG cycle:
 
The maximum norm of residuals after 49 times FMG cycle=2.81167e-05

The 49-th residual reduction rate is about 0.353213

The maximum norm of error after 49 times FMG cycle=2.74891e-06

The 50-th FMG cycle:
 
The maximum norm of residuals after 50 times FMG cycle=1.81962e-05

The 50-th residual reduction rate is about 0.352834

The maximum norm of error after 50 times FMG cycle=1.76821e-06

The 51-th FMG cycle:
 
The maximum norm of residuals after 51 times FMG cycle=1.17364e-05

The 51-th residual reduction rate is about 0.355005

The maximum norm of error after 51 times FMG cycle=1.13155e-06

The 52-th FMG cycle:
 
The maximum norm of residuals after 52 times FMG cycle=7.54115e-06

The 52-th residual reduction rate is about 0.357458

The maximum norm of error after 52 times FMG cycle=7.20701e-07

The 53-th FMG cycle:
 
The maximum norm of residuals after 53 times FMG cycle=4.82588e-06

The 53-th residual reduction rate is about 0.360061

The maximum norm of error after 53 times FMG cycle=4.56977e-07

The 54-th FMG cycle:
 
The maximum norm of residuals after 54 times FMG cycle=3.07639e-06

The 54-th residual reduction rate is about 0.362522

The maximum norm of error after 54 times FMG cycle=2.88609e-07

The 55-th FMG cycle:
 
The maximum norm of residuals after 55 times FMG cycle=1.95445e-06

The 55-th residual reduction rate is about 0.364696

The maximum norm of error after 55 times FMG cycle=1.81695e-07

The 56-th FMG cycle:
 
The maximum norm of residuals after 56 times FMG cycle=1.23859e-06

The 56-th residual reduction rate is about 0.366269

The maximum norm of error after 56 times FMG cycle=1.14072e-07

The 57-th FMG cycle:
 
The maximum norm of residuals after 57 times FMG cycle=7.82377e-07

The 57-th residual reduction rate is about 0.368335

The maximum norm of error after 57 times FMG cycle=7.13838e-08

The 58-th FMG cycle:
 
The maximum norm of residuals after 58 times FMG cycle=4.92779e-07

The 58-th residual reduction rate is about 0.370151

The maximum norm of error after 58 times FMG cycle=4.45445e-08

The 59-th FMG cycle:
 
The maximum norm of residuals after 59 times FMG cycle=3.09556e-07

The 59-th residual reduction rate is about 0.371816

The maximum norm of error after 59 times FMG cycle=2.78261e-08

The 60-th FMG cycle:
 
The maximum norm of residuals after 60 times FMG cycle=1.9429e-07

The 60-th residual reduction rate is about 0.372359

The maximum norm of error after 60 times FMG cycle=1.7431e-08

The 61-th FMG cycle:
 
The maximum norm of residuals after 61 times FMG cycle=1.20963e-07

The 61-th residual reduction rate is about 0.37741

The maximum norm of error after 61 times FMG cycle=1.08782e-08

The 62-th FMG cycle:
 
The maximum norm of residuals after 62 times FMG cycle=7.51302e-08

The 62-th residual reduction rate is about 0.378899

The maximum norm of error after 62 times FMG cycle=6.71026e-09

Obviously, the maximum norm of error has the first order convergence.

\section*{IV.Gradually reduce $\epsilon$ towards $ 2.2*10^{-16}$ , under which critical value of $\epsilon$ does your program fail to achieve the preset accuracy?Why?}

In the fourth question,we choose n=1025,injection,quadratic and FMG cycle.The results are as follows:

The 1-th FMG cycle:
 
The maximum norm of residuals after 1 times FMG cycle=228043

The 1-th residual reduction rate is about 0.953125

The maximum norm of error after 1 times FMG cycle=1.68553

The 2-th FMG cycle:
 
The maximum norm of residuals after 2 times FMG cycle=86612.5

The 2-th residual reduction rate is about 0.620192

The maximum norm of error after 2 times FMG cycle=2.58562

The 3-th FMG cycle:
 
The maximum norm of residuals after 3 times FMG cycle=39532.9

The 3-th residual reduction rate is about 0.543566

The maximum norm of error after 3 times FMG cycle=2.89094

The 4-th FMG cycle:
 
The maximum norm of residuals after 4 times FMG cycle=20440.6

The 4-th residual reduction rate is about 0.482948

The maximum norm of error after 4 times FMG cycle=3.72777

The 5-th FMG cycle:
 
The maximum norm of residuals after 5 times FMG cycle=9545.15

The 5-th residual reduction rate is about 0.53303

The maximum norm of error after 5 times FMG cycle=4.37941

The 6-th FMG cycle:
 
The maximum norm of residuals after 6 times FMG cycle=4743.87

The 6-th residual reduction rate is about 0.503007

The maximum norm of error after 6 times FMG cycle=6.87016

The 7-th FMG cycle:
 
The maximum norm of residuals after 7 times FMG cycle=2684.35

The 7-th residual reduction rate is about 0.434143

The maximum norm of error after 7 times FMG cycle=7.16302

The 8-th FMG cycle:
 
The maximum norm of residuals after 8 times FMG cycle=1464.45

The 8-th residual reduction rate is about 0.454451

The maximum norm of error after 8 times FMG cycle=5.63247

The 9-th FMG cycle:
 
The maximum norm of residuals after 9 times FMG cycle=988.037

The 9-th residual reduction rate is about 0.325316

The maximum norm of error after 9 times FMG cycle=3.57152

The 10-th FMG cycle:
 
The maximum norm of residuals after 10 times FMG cycle=675.475

The 10-th residual reduction rate is about 0.316347

The maximum norm of error after 10 times FMG cycle=3.2617

The 11-th FMG cycle:
 
The maximum norm of residuals after 11 times FMG cycle=415.123

The 11-th residual reduction rate is about 0.385435

The maximum norm of error after 11 times FMG cycle=3.10168

The 12-th FMG cycle:
 
The maximum norm of residuals after 12 times FMG cycle=233.705

The 12-th residual reduction rate is about 0.437023

The maximum norm of error after 12 times FMG cycle=2.69526

The 13-th FMG cycle:
 
The maximum norm of residuals after 13 times FMG cycle=134.447

The 13-th residual reduction rate is about 0.424715

The maximum norm of error after 13 times FMG cycle=2.19946

The 14-th FMG cycle:
 
The maximum norm of residuals after 14 times FMG cycle=76.1669

The 14-th residual reduction rate is about 0.433479

The maximum norm of error after 14 times FMG cycle=1.7143

The 15-th FMG cycle:
 
The maximum norm of residuals after 15 times FMG cycle=43.9327

The 15-th residual reduction rate is about 0.423205

The maximum norm of error after 15 times FMG cycle=1.34159

The 16-th FMG cycle:
 
The maximum norm of residuals after 16 times FMG cycle=27.1262

The 16-th residual reduction rate is about 0.38255

The maximum norm of error after 16 times FMG cycle=1.03892

The 17-th FMG cycle:
 
The maximum norm of residuals after 17 times FMG cycle=18.0065

The 17-th residual reduction rate is about 0.336197

The maximum norm of error after 17 times FMG cycle=0.781152

The 18-th FMG cycle:
 
The maximum norm of residuals after 18 times FMG cycle=11.4787

The 18-th residual reduction rate is about 0.362527

The maximum norm of error after 18 times FMG cycle=0.574774

The 19-th FMG cycle:
 
The maximum norm of residuals after 19 times FMG cycle=6.96409

The 19-th residual reduction rate is about 0.393301

The maximum norm of error after 19 times FMG cycle=0.416472

The 20-th FMG cycle:
 
The maximum norm of residuals after 20 times FMG cycle=4.16526

The 20-th residual reduction rate is about 0.401894

The maximum norm of error after 20 times FMG cycle=0.298346

The 21-th FMG cycle:
 
The maximum norm of residuals after 21 times FMG cycle=2.82193

The 21-th residual reduction rate is about 0.322508

The maximum norm of error after 21 times FMG cycle=0.211691

The 22-th FMG cycle:
 
The maximum norm of residuals after 22 times FMG cycle=2.02349

The 22-th residual reduction rate is about 0.282943

The maximum norm of error after 22 times FMG cycle=0.148824

The 23-th FMG cycle:
 
The maximum norm of residuals after 23 times FMG cycle=1.42118

The 23-th residual reduction rate is about 0.29766

The maximum norm of error after 23 times FMG cycle=0.103614

The 24-th FMG cycle:
 
The maximum norm of residuals after 24 times FMG cycle=0.978928

The 24-th residual reduction rate is about 0.311184

The maximum norm of error after 24 times FMG cycle=0.0713877

The 25-th FMG cycle:
 
The maximum norm of residuals after 25 times FMG cycle=0.660101

The 25-th residual reduction rate is about 0.32569

The maximum norm of error after 25 times FMG cycle=0.0486484

The 26-th FMG cycle:
 
The maximum norm of residuals after 26 times FMG cycle=0.43589

The 26-th residual reduction rate is about 0.339662

The maximum norm of error after 26 times FMG cycle=0.0327901

The 27-th FMG cycle:
 
The maximum norm of residuals after 27 times FMG cycle=0.282271

The 27-th residual reduction rate is about 0.352426

The maximum norm of error after 27 times FMG cycle=0.0218729

The 28-th FMG cycle:
 
The maximum norm of residuals after 28 times FMG cycle=0.179546

The 28-th residual reduction rate is about 0.363925

The maximum norm of error after 28 times FMG cycle=0.0144581

The 29-th FMG cycle:
 
The maximum norm of residuals after 29 times FMG cycle=0.113209

The 29-th residual reduction rate is about 0.36947

The maximum norm of error after 29 times FMG cycle=0.00948825

The 30-th FMG cycle:
 
The maximum norm of residuals after 30 times FMG cycle=0.0720004

The 30-th residual reduction rate is about 0.364004

The maximum norm of error after 30 times FMG cycle=0.00619752

The 31-th FMG cycle:
 
The maximum norm of residuals after 31 times FMG cycle=0.0452824

The 31-th residual reduction rate is about 0.37108

The maximum norm of error after 31 times FMG cycle=0.00404084

The 32-th FMG cycle:
 
The maximum norm of residuals after 32 times FMG cycle=0.0284444

The 32-th residual reduction rate is about 0.371845

The maximum norm of error after 32 times FMG cycle=0.00263802

The 33-th FMG cycle:
 
The maximum norm of residuals after 33 times FMG cycle=0.0177966

The 33-th residual reduction rate is about 0.374336

The maximum norm of error after 33 times FMG cycle=0.00172939

The 34-th FMG cycle:
 
The maximum norm of residuals after 34 times FMG cycle=0.0111206

The 34-th residual reduction rate is about 0.375125

The maximum norm of error after 34 times FMG cycle=0.00114104

The 35-th FMG cycle:
 
The maximum norm of residuals after 35 times FMG cycle=0.00693129

The 35-th residual reduction rate is about 0.376719

The maximum norm of error after 35 times FMG cycle=0.000758719

The 36-th FMG cycle:
 
The maximum norm of residuals after 36 times FMG cycle=0.00452312

The 36-th residual reduction rate is about 0.347435

The maximum norm of error after 36 times FMG cycle=0.000508562

The 37-th FMG cycle:
 
The maximum norm of residuals after 37 times FMG cycle=0.00324476

The 37-th residual reduction rate is about 0.282628

The maximum norm of error after 37 times FMG cycle=0.000343322

The 38-th FMG cycle:
 
The maximum norm of residuals after 38 times FMG cycle=0.00229824

The 38-th residual reduction rate is about 0.291706

The maximum norm of error after 38 times FMG cycle=0.000233124

The 39-th FMG cycle:
 
The maximum norm of residuals after 39 times FMG cycle=0.00160939

The 39-th residual reduction rate is about 0.299729

The maximum norm of error after 39 times FMG cycle=0.000159236

The 40-th FMG cycle:
 
The maximum norm of residuals after 40 times FMG cycle=0.00111528

The 40-th residual reduction rate is about 0.307019

The maximum norm of error after 40 times FMG cycle=0.000109037

The 41-th FMG cycle:
 
The maximum norm of residuals after 41 times FMG cycle=0.000765176

The 41-th residual reduction rate is about 0.313914

The maximum norm of error after 41 times FMG cycle=7.4417e-05

The 42-th FMG cycle:
 
The maximum norm of residuals after 42 times FMG cycle=0.000519973

The 42-th residual reduction rate is about 0.320453

The maximum norm of error after 42 times FMG cycle=5.04943e-05

The 43-th FMG cycle:
 
The maximum norm of residuals after 43 times FMG cycle=0.000350222

The 43-th residual reduction rate is about 0.326462

The maximum norm of error after 43 times FMG cycle=3.40251e-05

The 44-th FMG cycle:
 
The maximum norm of residuals after 44 times FMG cycle=0.00023399

The 44-th residual reduction rate is about 0.331882

The maximum norm of error after 44 times FMG cycle=2.27624e-05

The 45-th FMG cycle:
 
The maximum norm of residuals after 45 times FMG cycle=0.000155171

The 45-th residual reduction rate is about 0.336847

The maximum norm of error after 45 times FMG cycle=1.51178e-05

The 46-th FMG cycle:
 
The maximum norm of residuals after 46 times FMG cycle=0.000102176

The 46-th residual reduction rate is about 0.341524

The maximum norm of error after 46 times FMG cycle=9.96963e-06

The 47-th FMG cycle:
 
The maximum norm of residuals after 47 times FMG cycle=6.68448e-05

The 47-th residual reduction rate is about 0.34579

The maximum norm of error after 47 times FMG cycle=6.53001e-06

The 48-th FMG cycle:
 
The maximum norm of residuals after 48 times FMG cycle=4.34713e-05

The 48-th residual reduction rate is about 0.349668

The maximum norm of error after 48 times FMG cycle=4.24962e-06

The 49-th FMG cycle:
 
The maximum norm of residuals after 49 times FMG cycle=2.81167e-05

The 49-th residual reduction rate is about 0.353213

The maximum norm of error after 49 times FMG cycle=2.74891e-06

The 50-th FMG cycle:
 
The maximum norm of residuals after 50 times FMG cycle=1.81962e-05

The 50-th residual reduction rate is about 0.352834

The maximum norm of error after 50 times FMG cycle=1.76821e-06

The 51-th FMG cycle:
 
The maximum norm of residuals after 51 times FMG cycle=1.17364e-05

The 51-th residual reduction rate is about 0.355005

The maximum norm of error after 51 times FMG cycle=1.13155e-06

The 52-th FMG cycle:
 
The maximum norm of residuals after 52 times FMG cycle=7.54115e-06

The 52-th residual reduction rate is about 0.357458

The maximum norm of error after 52 times FMG cycle=7.20701e-07

The 53-th FMG cycle:
 
The maximum norm of residuals after 53 times FMG cycle=4.82588e-06

The 53-th residual reduction rate is about 0.360061

The maximum norm of error after 53 times FMG cycle=4.56977e-07

The 54-th FMG cycle:
 
The maximum norm of residuals after 54 times FMG cycle=3.07639e-06

The 54-th residual reduction rate is about 0.362522

The maximum norm of error after 54 times FMG cycle=2.88609e-07

The 55-th FMG cycle:
 
The maximum norm of residuals after 55 times FMG cycle=1.95445e-06

The 55-th residual reduction rate is about 0.364696

The maximum norm of error after 55 times FMG cycle=1.81695e-07

The 56-th FMG cycle:
 
The maximum norm of residuals after 56 times FMG cycle=1.23859e-06

The 56-th residual reduction rate is about 0.366269

The maximum norm of error after 56 times FMG cycle=1.14072e-07

The 57-th FMG cycle:
 
The maximum norm of residuals after 57 times FMG cycle=7.82377e-07

The 57-th residual reduction rate is about 0.368335

The maximum norm of error after 57 times FMG cycle=7.13838e-08

The 58-th FMG cycle:
 
The maximum norm of residuals after 58 times FMG cycle=4.92779e-07

The 58-th residual reduction rate is about 0.370151

The maximum norm of error after 58 times FMG cycle=4.45445e-08

The 59-th FMG cycle:
 
The maximum norm of residuals after 59 times FMG cycle=3.09556e-07

The 59-th residual reduction rate is about 0.371816

The maximum norm of error after 59 times FMG cycle=2.78261e-08

The 60-th FMG cycle:
 
The maximum norm of residuals after 60 times FMG cycle=1.9429e-07

The 60-th residual reduction rate is about 0.372359

The maximum norm of error after 60 times FMG cycle=1.7431e-08

The 61-th FMG cycle:
 
The maximum norm of residuals after 61 times FMG cycle=1.20963e-07

The 61-th residual reduction rate is about 0.37741

The maximum norm of error after 61 times FMG cycle=1.08782e-08

The 62-th FMG cycle:
 
The maximum norm of residuals after 62 times FMG cycle=7.51302e-08

The 62-th residual reduction rate is about 0.378899

The maximum norm of error after 62 times FMG cycle=6.71026e-09

The 63-th FMG cycle:
 
The maximum norm of residuals after 63 times FMG cycle=4.64571e-08

The 63-th residual reduction rate is about 0.381646

The maximum norm of error after 63 times FMG cycle=4.10431e-09

The 64-th FMG cycle:
 
The maximum norm of residuals after 64 times FMG cycle=2.96665e-08

The 64-th residual reduction rate is about 0.361421

The maximum norm of error after 64 times FMG cycle=2.49397e-09

The 65-th FMG cycle:
 
The maximum norm of residuals after 65 times FMG cycle=2.01769e-08

The 65-th residual reduction rate is about 0.319876

The maximum norm of error after 65 times FMG cycle=1.46876e-09

The 66-th FMG cycle:
 
The maximum norm of residuals after 66 times FMG cycle=1.29376e-08

The 66-th residual reduction rate is about 0.358792

The maximum norm of error after 66 times FMG cycle=8.07466e-10

The 67-th FMG cycle:
 
The maximum norm of residuals after 67 times FMG cycle=8.15788e-09

The 67-th residual reduction rate is about 0.369443

The maximum norm of error after 67 times FMG cycle=4.25002e-10

The 68-th FMG cycle:
 
The maximum norm of residuals after 68 times FMG cycle=5.46816e-09

The 68-th residual reduction rate is about 0.329709

The maximum norm of error after 68 times FMG cycle=2.03851e-10

The 69-th FMG cycle:
 
The maximum norm of residuals after 69 times FMG cycle=3.8836e-09

The 69-th residual reduction rate is about 0.289778

The maximum norm of error after 69 times FMG cycle=6.83548e-11

The 70-th FMG cycle:
 
The maximum norm of residuals after 70 times FMG cycle=4.4706e-09

The 70-th residual reduction rate is about -0.151148

The maximum norm of error after 70 times FMG cycle=9.97172e-11

The 71-th FMG cycle:
 
The maximum norm of residuals after 71 times FMG cycle=4.4866e-09

The 71-th residual reduction rate is about -0.00357878

The maximum norm of error after 71 times FMG cycle=1.5996e-10

The 72-th FMG cycle:
 
The maximum norm of residuals after 72 times FMG cycle=3.71076e-09

The 72-th residual reduction rate is about 0.172925

The maximum norm of error after 72 times FMG cycle=1.14607e-10

The 73-th FMG cycle:
 
The maximum norm of residuals after 73 times FMG cycle=3.05402e-09

The 73-th residual reduction rate is about 0.176982

The maximum norm of error after 73 times FMG cycle=6.99439e-11

The 74-th FMG cycle:
 
The maximum norm of residuals after 74 times FMG cycle=4.82424e-09

The 74-th residual reduction rate is about -0.579634

The maximum norm of error after 74 times FMG cycle=2.00641e-10

The 75-th FMG cycle:
 
The maximum norm of residuals after 75 times FMG cycle=3.55767e-09

The 75-th residual reduction rate is about 0.262543

The maximum norm of error after 75 times FMG cycle=2.29553e-10

The 76-th FMG cycle:
 
The maximum norm of residuals after 76 times FMG cycle=3.01877e-09

The 76-th residual reduction rate is about 0.151475

The maximum norm of error after 76 times FMG cycle=2.2715e-10

The 77-th FMG cycle:
 
The maximum norm of residuals after 77 times FMG cycle=2.67127e-09

The 77-th residual reduction rate is about 0.115113

The maximum norm of error after 77 times FMG cycle=1.86739e-10

The 78-th FMG cycle:
 
The maximum norm of residuals after 78 times FMG cycle=2.75972e-09

The 78-th residual reduction rate is about -0.0331141

The maximum norm of error after 78 times FMG cycle=1.21292e-10

The 79-th FMG cycle:
 
The maximum norm of residuals after 79 times FMG cycle=2.82821e-09

The 79-th residual reduction rate is about -0.0248163

The maximum norm of error after 79 times FMG cycle=7.00459e-11

The 80-th FMG cycle:
 
The maximum norm of residuals after 80 times FMG cycle=3.04234e-09

The 80-th residual reduction rate is about -0.0757127

The maximum norm of error after 80 times FMG cycle=6.21629e-11

The 81-th FMG cycle:
 
The maximum norm of residuals after 81 times FMG cycle=3.2303e-09

The 81-th residual reduction rate is about -0.061779

The maximum norm of error after 81 times FMG cycle=1.32725e-10

The 82-th FMG cycle:
 
The maximum norm of residuals after 82 times FMG cycle=3.33391e-09

The 82-th residual reduction rate is about -0.0320771

The maximum norm of error after 82 times FMG cycle=1.83021e-10

The 83-th FMG cycle:
 
The maximum norm of residuals after 83 times FMG cycle=3.50293e-09

The 83-th residual reduction rate is about -0.0506964

The maximum norm of error after 83 times FMG cycle=1.947e-10

The 84-th FMG cycle:
 
The maximum norm of residuals after 84 times FMG cycle=3.37777e-09

The 84-th residual reduction rate is about 0.0357305

The maximum norm of error after 84 times FMG cycle=1.42507e-10

The 85-th FMG cycle:
 
The maximum norm of residuals after 85 times FMG cycle=4.66808e-09

The 85-th residual reduction rate is about -0.382

The maximum norm of error after 85 times FMG cycle=8.01741e-11

The 86-th FMG cycle:
 
The maximum norm of residuals after 86 times FMG cycle=4.06691e-09

The 86-th residual reduction rate is about 0.128783

The maximum norm of error after 86 times FMG cycle=6.34992e-11

The 87-th FMG cycle:
 
The maximum norm of residuals after 87 times FMG cycle=5.15597e-09

The 87-th residual reduction rate is about -0.267785

The maximum norm of error after 87 times FMG cycle=8.53737e-11

The 88-th FMG cycle:
 
The maximum norm of residuals after 88 times FMG cycle=4.4367e-09

The 88-th residual reduction rate is about 0.139503

The maximum norm of error after 88 times FMG cycle=1.18217e-10

The 89-th FMG cycle:
 
The maximum norm of residuals after 89 times FMG cycle=3.42404e-09

The 89-th residual reduction rate is about 0.228245

The maximum norm of error after 89 times FMG cycle=1.59095e-10

The 90-th FMG cycle:
 
The maximum norm of residuals after 90 times FMG cycle=2.92517e-09

The 90-th residual reduction rate is about 0.145696

The maximum norm of error after 90 times FMG cycle=1.92859e-10

The 91-th FMG cycle:
 
The maximum norm of residuals after 91 times FMG cycle=3.4059e-09

The 91-th residual reduction rate is about -0.164344

The maximum norm of error after 91 times FMG cycle=1.13959e-10

The 92-th FMG cycle:
 
The maximum norm of residuals after 92 times FMG cycle=3.64255e-09

The 92-th residual reduction rate is about -0.0694817

The maximum norm of error after 92 times FMG cycle=7.85716e-11

The 93-th FMG cycle:
 
The maximum norm of residuals after 93 times FMG cycle=3.95389e-09

The 93-th residual reduction rate is about -0.085472

The maximum norm of error after 93 times FMG cycle=2.22344e-10

The 94-th FMG cycle:
 
The maximum norm of residuals after 94 times FMG cycle=4.26736e-09

The 94-th residual reduction rate is about -0.0792805

The maximum norm of error after 94 times FMG cycle=2.3399e-10

The 95-th FMG cycle:
 
The maximum norm of residuals after 95 times FMG cycle=3.18323e-09

The 95-th residual reduction rate is about 0.254052

The maximum norm of error after 95 times FMG cycle=1.99383e-10

The 96-th FMG cycle:
 
The maximum norm of residuals after 96 times FMG cycle=2.99581e-09

The 96-th residual reduction rate is about 0.0588763

The maximum norm of error after 96 times FMG cycle=1.8782e-10

The 97-th FMG cycle:
 
The maximum norm of residuals after 97 times FMG cycle=3.5131e-09

The 97-th residual reduction rate is about -0.17267

The maximum norm of error after 97 times FMG cycle=1.80647e-10

The 98-th FMG cycle:
 
The maximum norm of residuals after 98 times FMG cycle=3.7657e-09

The 98-th residual reduction rate is about -0.071904

The maximum norm of error after 98 times FMG cycle=1.96788e-10

The 99-th FMG cycle:
 
The maximum norm of residuals after 99 times FMG cycle=4.22376e-09

The 99-th residual reduction rate is about -0.121639

The maximum norm of error after 99 times FMG cycle=2.52805e-10

The 100-th FMG cycle:
 
The maximum norm of residuals after 100 times FMG cycle=4.44325e-09

The 100-th residual reduction rate is about -0.0519657

The maximum norm of error after 100 times FMG cycle=2.827e-10

We find that when the maximum norm of the error reaches $10^{-10}$, it no longer decreases.There are three main problems. First, the number of nodes. We may not select enough nodes. Second, our maximum number of iterations is limited, which can only be iterated 100 times in my program. Third, there are errors in the algorithm itself, such as interpolation and limited time.

\section*{V.Design a test with homogeneous boundary conditions and repeat III.  }

We choose $u(x)=sin(x)*sin(1-x)$.The result is similar to the third question, which can be seen in the program, so there is no repetition here.

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